JP6979732B1 - Programs, methods and information processing equipment for predicting the average of variable interest rates - Google Patents

Abstract

Realize empirical average interest rate forecasts. The program generates the interest rate transition frequency from the past interest rate (X1-X4); reads the initial interest rate among multiple interest rates; sees the first interest rate, the first approximate cumulative average interest rate, and the first cumulative transition path number in the previous period. Then, the second interest rate of the transition destination from the first interest rate and the interest rate transition frequency are determined by referring to the interest rate transition frequency data, and the first approximate cumulative average interest rate of the previous period and the second interest rate of the period of interest to the second interest rate of the period of interest are determined. Find the cumulative average interest rate for 2 interest rates, determine the 2nd approximate cumulative average interest rate of 1 or 2 among the multiple interest rates closest to the cumulative average interest rate, and transition to the 2nd interest rate in the number of 1st cumulative transition paths in the previous period. Multiply the frequency to obtain the second cumulative transition path number, and add at least a part of the second cumulative transition path number to the second cumulative transition path number related to the second interest rate and the second approximate cumulative average interest rate during the period of interest, and the second interest rate. , The process of setting the second approximate cumulative average interest rate and the third cumulative transition path number as the next first interest rate, the first approximate cumulative average interest rate, and the first cumulative transition path number in the period preceding the next period of interest, respectively, is repeated.

Description

The present invention relates to processing for predicting the average of variable interest rates.

Generally, interest rates on corporate bonds are fixed until the maturity date. On the other hand, short-term lending rates of banks fluctuate once every few months depending on the interest rate situation. A common concern about corporate bonds is the gains and losses when comparing the interest burden on corporate bonds in the period to redemption with the repetitive short-term borrowing from banks. Currently, experienced experts often examine the experience and past data of the Bank of Japan to estimate the interest burden on corporate bonds and short-term borrowings by assuming several patterns of interest rate fluctuations, generally subjectively. It takes years to train such professionals. There are also disagreements among experts, but the reason is not clear.

Scientific methods of interest rate analysis include multiple methods based on the validity of the theory of extension of normal distribution called random walk and the theory of binomial distribution that defines and develops constant ups and downs. Such a theory may be suitable for things that fluctuate from moment to moment, such as the stock market. It is known, for example, in the literature: Eugene Fama, Merton H. Miller "The Theory of Finance" Dryden Press, p. 339-340.

For example, the expected value of the average interest rate when borrowing funds at a fluctuating bank short-term interest rate over a fixed period of 10 years is calculated by randomly changing the bank short-term interest rate using the Monte Carlo simulation method. Can be done. It is known, for example, in the literature: Sheldon M. Ross "Simulation, fifth edition" Academic Press, p. 271-274.

Japanese Patent No. 6470617 of the present inventor describes a program for obtaining the probability of predicting the average interest rate for a certain period in the future according to the transition probability of the interest rate. _{The program finds the second average interest rate (X k} ) up to the period of interest for each combination of the first average interest rate (Z _q ) and the second interest rate (X _j ), and is close to the second average interest rate. The third average interest rate (Z _k ) in the average interest rate is determined, and based on the probability of occurrence of the first average interest rate with respect to the first interest rate and the transition probability from the first interest rate to the second interest rate. The probability of occurrence of the second interest rate for each combination of the first interest rate and the first average interest rate is calculated as the probability of occurrence of the second average interest rate, and at least a part of the probability of occurrence of the second average interest rate for the second interest rate. Is calculated as the probability of occurrence of the third average interest rate for the second interest rate, and the probability of occurrence of the third average interest rate for the second interest rate in the period of interest is equal to the second interest rate in the period preceding the next period of interest. The process of setting as the occurrence probability of the first average interest rate equal to the third interest rate with respect to the first interest rate is repeated for each period, and the occurrence probability of each average interest rate in the last period is displayed.

Patent No. 6470617

Eugene Fama, Merton H. Miller "The Theory of Finance" Dryden Press, p.339-340 Sheldon M. Ross "Simulation, fifth edition" Academic Press, p.271-274

However, the inventor recognized that Japanese Patent No. 6470617 has a problem of how to rationally determine the transition probability.

An object of the present invention is to realize a method for predicting an average interest rate based on experience. Another object of the present invention is to determine in an information processing apparatus the possible number of occurrences of each predicted value of the average interest rate in a certain period in the future according to the fluctuation or transition frequency of the actual interest rate in the past. Another object of the present invention is to enable an information processing apparatus to obtain the possible number of possible occurrences of each predicted value of the average interest rate in a certain period in the future in a short time.

Overview of the Invention According to one aspect of the embodiment, the program for predicting the average of variable interest rates represents the frequency of interest rate transitions in adjacent periods based on multiple interest rates over at least a series of past periods. Generates an interest rate transition and stores it in the storage; reads the number of periods of multiple periods and the initial interest rate selected from multiple interest rates as the interest rate of the initial period and the approximate cumulative average interest rate, and multiple periods. With reference to the first interest rate in the period before the period of interest, the first approximate cumulative average interest rate for the first interest rate, and the number of first cumulative transition paths for the first interest rate in the storage unit, the interest rate transition With reference to the frequency, the second interest rate to which the transition from the first interest rate is made and the transition frequency thereof are determined, and the first approximate cumulative average interest rate for the first interest rate in the previous period and the second in the period of interest are used. From the interest rate, the cumulative average interest rate for the second interest rate of the period of interest is obtained, and one or two second approximate cumulative average interest rates among the multiple interest rates closest to the obtained cumulative average interest rate are determined, and here. The first and second interest rates and the first and second approximate cumulative average interest rates are any of a plurality of interest rates, and the first cumulative transition path for the first interest rate in the previous period. The number is multiplied by the transition frequency to obtain the number of second cumulative transition paths, and at least a portion of the number of second cumulative transition paths is the corresponding second interest rate for the period of interest and the corresponding second approximate cumulative average interest rate. It is added to the number of cumulative transition paths of 3 and stored in the storage unit, and the second interest rate, the second approximate cumulative average interest rate, and the number of the third cumulative transition paths are set after the period before the next period of interest, respectively. 1st interest rate, the next 1st approximate cumulative average interest rate for the next 1st interest rate, and the process used as the next 1st cumulative transition path number for the next 1st interest rate; Let the information processing device execute the processing. The program may be stored on a non-temporary computer-readable medium.

In embodiments, the program may further include processing to display the sum of the number of third cumulative transition paths for each of the second approximate cumulative average interest rates in the last period of the plurality of periods.

In the embodiment, the calculated cumulative average interest rate obtained up to the period of interest for each combination of the first approximate cumulative average interest rate and the second interest rate in the previous period is the first approximate cumulative average interest rate and the previous period. It may be obtained by dividing the product of the number of periods and the sum of the second interest rates by the number of periods up to the period of interest.

In the embodiment, when the second approximate cumulative average interest rate closest to the calculated cumulative average interest rate is the third approximate cumulative average interest rate and the fourth approximate cumulative average interest rate, the second approximate cumulative average interest rate with respect to the calculated cumulative average interest rate. A part of the cumulative transition paths is added to the third cumulative transition paths for the second interest rate and the third approximate cumulative average interest rate, and the rest of the second cumulative transition paths is the second interest rate and the second cumulative transition paths. It may be added to the number of third cumulative transition paths for the approximate cumulative average interest rate of 4.

In the embodiment, a part of the second cumulative transition path number to be added to the third cumulative transition path number for the second interest rate and the third approximate cumulative average interest rate is the obtained cumulative average interest rate and the third cumulative transition path. It may tend to increase as the difference between the approximate cumulative average interest rates decreases.

According to another aspect of the embodiment, the program for predicting the average of variable interest rates is an interest rate transition that represents the frequency of interest rate transitions in adjacent periods based on multiple interest rates in at least a series of past periods. Generates frequency data and generates and stores interest rate transition probabilities from multiple interest rates to multiple interest rates based on interest rate transition frequency data; multiple periods and interest rates and approximate cumulative averages for the initial period. The initial interest rate selected from a plurality of interest rates is read as the interest rate, and for the plurality of periods, the first interest rate of the period before the period of interest and the first approximate cumulative average of the first interest rates in the storage unit. With reference to the interest rate and the first cumulative transition probability for the first interest rate, and with reference to the interest rate transition probability, the second interest rate to which the transition from the first interest rate is made and its transition probability are determined, and the previous period From the first approximate cumulative average interest rate for the first interest rate and the second interest rate for the period of interest, the cumulative average interest rate for the second interest rate for the period of interest is calculated, and among the multiple interest rates closest to the obtained cumulative average interest rate. One or two second approximate cumulative average interest rates of, where the first and second interest rates and the first and second approximate cumulative average interest rates are interest rates of any of a plurality of interest rates. Further, the first cumulative transition probability for the first interest rate in the previous period is multiplied by the transition probability to obtain the second cumulative transition probability, and at least a part of the second cumulative transition probability is obtained in the period of interest. Add to the corresponding third cumulative transition probability for the second interest rate and the second approximate cumulative average interest rate and store in the storage, the second interest rate, the second approximate cumulative average interest rate and the third cumulative transition. The probabilities are the next first interest rate for the period preceding the next period of interest, the next first approximate cumulative average interest rate for the next first interest rate, and the next first for the next first interest rate, respectively. Repeating the process used as the cumulative transition probability of; causes the information processing apparatus to execute the process including. The program may be stored on a non-temporary computer-readable medium.

According to the embodiment, the information processing apparatus can determine the possible number of occurrences of each predicted value of the average interest rate in a certain period in the future according to the frequency of the actual fluctuation or transition of the actual interest rate in the past, and each prediction thereof. The number of values generated can be obtained in a short time.

FIG. 1 shows an example of a schematic configuration of an information processing apparatus according to an embodiment. FIG. 2 shows an example of a schematic configuration of a system including an information processing device and a server device according to an embodiment. FIG. 3 shows an example of a schematic configuration of a processor of an information processing device. FIG. 4A shows an example of past monthly interest rates. FIG. 4B shows an example of a monthly interest rate transition. FIG. 4C shows an example of a table of interest rate transition frequencies from the interest rate of each previous month to the interest rate of each current month. FIG. 5A shows another example of past monthly interest rates. FIG. 5B shows another example of the monthly interest rate transition. FIG. 5C shows an example of another table of interest rate transition frequencies from the interest rate of each previous month to the interest rate of each current month. FIG. 6A shows an example of a flowchart of processing executed by the information processing apparatus to generate a table of interest rate transition frequencies from a plurality of interest rates in a past series of periods. 6B and 6C are examples of processing flowcharts for determining the possible number of occurrences of each average interest rate for a period starting at the initial monthly interest rate and at the end of the period number, after the flowchart of FIG. 6A. Shows. .. 7A-7C show the initial interest rate and the average interest rate, the interest rate and the average interest rate for each period after the interest rate transition, and the corresponding interest rate and the approximate average interest rate based on the interest rate transition frequency table according to the embodiment. An example of the transition diagram is shown. .. .. 8A-8G show the approximate cumulative average interest rate and the cumulative path using the monthly interest rate / approximate average interest rate / cumulative pass number table and the previous month interest rate / cumulative average interest rate / current month interest rate work record according to the flowcharts of FIGS. 6B and 6C. An example of the procedure for determining the rate of occurrence of a combination of numbers is shown. .. .. .. 9A and 9C show an example of an interest rate transition probability matrix T representing the transition probability from each past monthly interest rate to the next monthly interest rate according to another embodiment. FIG. 9B shows an example of a table of interest rate transition probabilities generated according to the table of interest rate transition frequencies in FIG. 4C. 10A and 10B are examples of a flow chart of processing to determine the possible cumulative probability of each average interest rate for a period starting at the initial monthly interest rate and at the end of the number of periods after the flow chart of FIG. 6A. Shows. .. FIG. 11 is an example of a transition diagram from the initial interest rate and the average interest rate to the interest rate and the average interest rate for each period after the interest rate transition, and further to the corresponding interest rate and the approximate average interest rate, based on the interest rate transition probability according to the embodiment. Is shown. FIG. 12A shows an example of a table of monthly interest rate / approximate average interest rate / cumulative probability in the initial period. 12B and 12C show an example of a work record of the previous month's interest rate / approximate average interest rate / current month's interest rate.

The objects and advantages of the invention are realized and achieved by the components and combinations specifically described in the claims. Non-limiting embodiments of the present invention will be described with reference to the drawings. In the drawings, similar components are given the same reference numbers.

The inventor recognized that Japanese Patent No. 6470617 has an unsolved problem of how to reflect the experience data on past interest rate transitions in the transition probability. Further, in Japanese Patent No. 6470617, the inventor cannot know the total number of cumulative passes of each approximate cumulative average interest rate in the prediction period, and the calculation accuracy is low by approximating the occurrence probability of each approximate cumulative average interest rate. I recognized the issue of becoming.

By limiting the predicted value of the possible interest rate transition path to a plurality of actual data experienced in the past, the inventor can obtain each predicted value of the average interest rate in a period of 120 or more, for example, by using a personal computer. I realized that it can be calculated in a short time.

An object of the embodiment is to calculate with an information processing apparatus the probability of occurrence of each predicted average interest rate for a future period according to the interest rate transition frequency based on past experience. Another object of the embodiment is to allow a personal computer to calculate the probability of occurrence of each predicted average interest rate for a future period in a shorter time according to the interest rate transition frequency data.

FIG. 1 shows an example of a schematic configuration of an information processing apparatus 10 according to an embodiment.

In FIG. 1, the information processing apparatus 10 may be, for example, a desktop type, a laptop type, a notebook type, or a tablet type personal computer, or a high-performance electronic desk computer or a smartphone. The information processing apparatus 10 includes, for example, a processor 102, a storage unit 104, an internal bus, a network interface (NW / IF) 108, an input unit 122, a display unit 124, and an acoustic unit 126. The network interface 108 can be connected to the network 5.

The information processing device 10 can be connected to an external drive (not shown). The external drive may be for reading a recording medium such as an optical disc or magnetic disk on which the software is recorded. The software may include, for example, an OS, a database management system (DBMS), an application program, and the like. The application program may include an application for calculating the average interest rate. The storage unit 104 may include a database.

The processor 102 may be a CPU (Central Processing Unit) for a computer. The storage unit 104 includes, for example, a semiconductor memory such as a ROM, a RAM, an SD (secure digital) memory or a flash memory such as a USB memory, an SSD (Solid State Drive), and / or a hard disk drive (HDD). It may be included.

The processor 102 may be a dedicated processor implemented as an integrated circuit, for example. Further, the processor 102 may operate according to the application program stored in the storage unit 104. The application program may be stored in the recording medium, read from the recording medium by an external drive, and installed in the information processing apparatus 10.

The input unit 122 may include, for example, a plurality of keys, a touch pad, a numeric keypad, a keyboard, a touch panel, and / or a pointing device. The display unit 124 may be, for example, a liquid crystal display device or an organic EL display device. The acoustic unit 126 may include, for example, a microphone, a speaker, and a receiver.

FIG. 2 shows an example of a schematic configuration of a system 2 including an information processing device 10 and a server device 20 according to an embodiment.

The system 2 includes an information processing device 10 and a server device 20 connected to the network 5. The network 5 may be, for example, an intranet or an IP (Internet Protocol) network such as a LAN or the Internet. The server device 20 and the information processing device 10 may be the server and the client of the server-client system, respectively.

The server device 20 is an information processing device and may be a computer including, for example, a processor 202, a memory 204, an internal bus, a storage device 206, and a network interface (NWI / F) 208. Further, the server device 20 may include, for example, one or more server units or server blades.

The server device 20 can be connected to an external drive (not shown). The external drive may be for reading a recording medium on which software is recorded, such as an optical disc or magnetic disk. The software may include, for example, an OS, a database management system (DBMS), an application program, and the like. The application program may include an application for calculating the average interest rate. The storage device 206 may include a database. The database in the storage device 206 of the server device 20 may include at least a part of the database in the storage unit 104 of the information processing device 10 of FIG. The storage unit 104 of the information processing device 10 of FIG. 1 may include a memory and a storage device corresponding to the memory 204 and the storage device 206 of the server device 20 of FIG. 2, respectively.

The processor 202 may be a CPU for a computer. The memory 204 includes, for example, a main storage device, a semiconductor memory, and the like. The storage device 206 may include, for example, a semiconductor memory such as a flash memory such as an SSD, SD memory or a USB memory, and / or a hard disk drive.

The processor 202 may be a dedicated processor implemented as an integrated circuit, for example. Further, the processor 202 may operate according to the application program stored in the memory 204 as a storage unit and / or the storage device 206. The application program may be stored in the recording medium, read from the recording medium by an external drive, and installed in the server device 20.

FIG. 3 shows an example of a schematic configuration of the processor 102 of the information processing apparatus 10.

In FIG. 3, the processor 102 includes a control unit 1020, an application unit 1024, a condition setting unit 1026, an interest rate transition frequency generation unit 1028, a cumulative path number calculation unit 1029, a display processing unit 1032, and other processing units 1040. .. The processor 102 may additionally include an interest rate transition probability generation unit 1030 and an average interest rate probability calculation unit 1031 in place of the interest rate transition frequency generation unit 1028 and the cumulative number of paths calculation unit 1029. The control unit 1020 may supply control signals to the elements 1024 to the processing unit 1040 to control the operation of these elements.

The information processing device 10 may operate as a client in a server-client system. In this case, the server device 20 may operate as a server in the server-client system and execute at least a part or all of the functions of the software for the information processing device 10 of FIG.

Next, two examples will be described of generating multiple records of interest rate transition frequencies representing the frequency of each interest rate transition in adjacent periods or months based on interest rates over a series of past periods.

FIG. 4A shows an example of a series of past changes in monthly interest rates. During the 9-month period shown in Figure 4A, the monthly interest rate rose from the initial value of 1.0% to 1.2%, then fell to 1.1%, then rose to 1.3%, and then to 1.2%. Go down. FIG. 4B shows an example of past monthly interest rate transitions generated from the transition of the monthly interest rate of FIG. 4A. Month rate transition are those disposed on the interest rate (X _p) from the rate transition of two adjacent month time to interest (X _q) of the current month (t) sequentially in each previous month (t-1). Figure 4C interest (X _p) from the rate transition frequency data representing the transition frequency or transition occurrence number T to interest (X _q) of the current month (t) past the previous month (t-1) in FIG. 4B An example of the table is shown. Therefore, the table in FIG. 4C represents past experience derived from the monthly interest rate data in FIG. 4A. The table of interest rate transition frequency shows the number of occurrences of a pair of the _{previous month's interest rate (X p} ) and each current month's interest rate (X _q ) in the past monthly interest rate transition in ascending order of the _{previous month's interest rate (X p} ) and the current month's interest rate (X _q). The transition frequency (T) is counted by sorting into. For example, the transition frequency from the previous month interest rate X _p = 1.0% to the current month interest rate X _q = 1.0% is 1 (times), and the previous month interest rate X _p = 1.1% to the current month interest rate X _q = 1. The transition frequency to 2% is 2 (times).

FIG. 5A shows another example of a series of past changes in monthly interest rates. During the period of 24 months in Figure 5A, the monthly interest rate rose from the initial value of 0.8% to 1.2%, then fell to 0.2%, then rose to 0.3%, and then to 0.2%. Go down. FIG. 5B shows an example of past monthly interest rate transitions generated from the transition of the monthly interest rate of FIG. 5A. Figure 5C is a rate (X _p) from the rate transition frequency data representing the transition frequency or transition occurrence number T to interest (X _q) of the current month (t) past the previous month (t-1) in FIG. 5B An example of the table is shown. Therefore, the table in FIG. 5C represents past experience derived from the monthly interest rate data in FIG. 5A. In this case, for example, the transition frequency from the previous month's interest rate of 0.2% to the current month's interest rate of 0.2% is 1, and the transition frequency from the previous month's interest rate X _p = 0.3% to the current month's interest rate X _q = 0.3%. Is 1. In the table of FIG. 5C, there is no transition from the monthly interest rate of 1.1% to the next month interest rate of 1.0%, and there is no transition from the monthly interest rate of 1.3% to the next month interest rate of 1.3%. In addition, in the interest rate transition frequency table, neither 0.4% nor 0.9% exists in a series of interest rates of 0.2 to 1.2% in 0.1% increments.

As long as there is continuity in the generated interest rate transitions, one of the interest rate transition frequency data representing the transition frequency or the number of transition occurrences T from two or more past monthly interest rates in periods separated from each other, for example, FIGS. 4A and 5A. You may generate two tables.

Next, using the interest rate transition frequency table in FIG. 4C or 5C, what is the cumulative transition path number (hereinafter, also referred to as “cumulative pass number”) P _{t of each interest rate from the initial interest rate to each subsequent month t?} It will be explained next whether it is predicted.

Here, a unit period or a time interval will be described as one month as an example. However, the unit period may be another time length such as 1 day, 7 days, 10 days, or 2 months. _{Further, let X q} be the qth interest rate (short-term interest rate) that can be taken in the current month or the month of interest t, which is the t-th period. Here, the sequence number t of the month t is t = 0, 1, 2, ... .. .. Let it be M. _{The qth interest rate X q} that can be obtained in t of the current month is X _q = x ₁ , x ₂ , ... .. .. x _N , q = 1, 2, ... .. .. Let it be N. On the other hand, p-th rate that can be taken in the previous month t-1 a (short-term interest rate) and X _{p. The p-th interest rate X p} that can be taken in the month t-1 is X _p = x ₁ , x ₂ . .. .. x _N , p = 1, 2, ... .. .. Let it be N. For the current month interest rate X _q , the cumulative average interest rate as of the current month t in the period from the first month 0 to the current month t is expressed _{as Y q. Further, let Z z} be the z-th approximate cumulative average interest rate close to the cumulative average interest rate Y _q. Here, the N approximate cumulative average interest rates (hereinafter, also referred to as “approximate average interest rates”) Z _z that can be taken are Z _z = x ₁ , x ₂ , ... .. .. x _N , z = 1, 2, ... .. .. Let it be N. _{The interest rate X q} in the current month t and the approximate cumulative average interest rate Z _{z regarding the interest rate X q} and the cumulative average interest rate Y _{q are the interest rate X p} and the approximate cumulative average interest rate of the previous month t-1 in the next month t (= t + 1), respectively. Used as Z _z.

7A-7C show the interest rate of each month t from the pair _{of the initial interest rate X 0 of the} first month t = 0 and the initial cumulative average interest rate Z ₀ based on the interest rate transition frequency table 700 of FIG. 4C according to the embodiment. An example of the transition or mapping between X _q and the cumulative average interest rate Y _q to each pair, and the interest rate X _q and the approximate cumulative average interest rate Z _{z to each pair is shown.}

The cumulative number of transition paths for the current month t interest rate X _q and the cumulative average interest rate Y _{q p t} = P (X _q , Y _q ) is the cumulative number of transition paths for the _{interest rate X p} and the cumulative average interest rate Z _z of the previous month t-1. The product of P _t-1 = P (X _p , Z _z ) and the transition frequency T (X _p , X _{q ) from the interest rate X p} of the previous month t-1 to the interest _{rate X q of the} current month t is as follows. It is expressed as.
P _t = P (X _q , Y _q ) = P _t-1 × T (X _p , X _q ) = P (X _p , Z _z ) × T (X _p , X _q )

In FIG. 7A, in the initial state 702 of the first month t = 0, the initial interest rate is X ₀ = X ₂ = 1.1%, and the initial cumulative average interest rate is Z ₀ = X ₀ = 1.1%. _{The initial value} of the cumulative transition paths for the initial interest rate X ₀ and the cumulative average interest rate Z _{0 is P 0} = P (X ₀ , Z ₀ ) = 1. For the initial interest rate X _{0 , the value of the previous month interest rate X p in} Table 700 of the interest rate transition frequency in FIG. 4C is selected.

In the next month t = 1, referring to Table 700 of interest transition frequency (Fig. 4C), as a transition destination from the previous month rate X ₂ = 1.1% of the initial state 702, the current month rate X ₂ = 1.1% The state 704 of (transition frequency 1) and the state 705 of the current month interest rate X ₃ = 1.2% (transition frequency 2) are obtained.

In state 704, the cumulative average interest rate Y _q for the current month interest rate X ₂ = 1.1% for the current month t = 1 is the cumulative average interest rate Z ₀ = 1.1% for the previous month t = 0 and the current month interest rate X _q = X ₂ =. From 1.1%, _{it is calculated as Y q} = Y ₂ = (Z ₀ × t + X ₂ ) / (t + 1) = (1.1 × 1 + 1.1) / 2 = 1.1%. The cumulative number of passes from the initial state 702 to the state 704 (current month interest rate X ₂ = 1.1%, cumulative average interest rate Y ₂ = 1.1%) is P _{t = 1} = P (X ₂ , Y ₂ ). It is the product of the total cumulative number of transition paths P _{q, z} = P ₀ = 1 for the month t = 0 and the transition frequency T (X ₂ , X ₂ ) = 1 from the previous month interest rate X ₀ to the current month interest rate X _2. It is calculated as P ₀ × T (X ₂ , X ₂ ) = 1 × 1 = 1. The total number of cumulative transition paths is also hereinafter referred to as “total total number of cumulative paths”.

In state 705, the cumulative average interest rate Y _q for the current month interest rate X ₃ = 1.2% for the current month t = 1 is the cumulative average interest rate Z ₀ = 1.1% for the previous month t = 0 and the current month interest rate X _q = X ₃ =. From 1.2%, _{it is calculated as Y q} = Y ₃ = (Z ₀ × t + X ₂ ) / (t + 1) = (1.1 × 1 + 1.2) / 2 = 1.15% (hereinafter, display “%”. May be omitted). The cumulative number of paths from the initial state 702 to the state 705 (X ₃ = 1.2, Y _{3 = 1.15) P t = 1} = P ₁ (X ₃ , Y ₃ ) is the sum of the months t = 0. It is the product of the cumulative number of passes P _{q, z} = P ₀ = 1 and the transition frequency T (X ₂ , X ₃ ) = 2 from the previous month's interest rate X ₀ to the current month's interest rate X _{3 , and is P 0} × T (X _2). , X ₃ ) = 1 × 2 = 2.

The states 704 and 705 are then transitioned or mapped by approximation to states 706 and 707 containing the approximate cumulative average interest rate Z _z closest to each cumulative average interest rate Y _{q at each interest rate X q, respectively.} Here, Y _q = Z _z or ≈ Z _z . The number of pairs of interest X _q approximated cumulative average rate Z _z is the square Namely N × N number of number N of past interest x ₁ ~x _N at maximum.

In the state 706 (X _q = X ₂ = 1.1, Z _z = Z ₂ = 1.1), the cumulative number of passes P _t = P (X ₂ , Y ₂ ) = 1 is approximately cumulative with the monthly interest rate X _q. It is added to the total cumulative number of _{passes P q, z} (initial value 0) for one pair of the average interest rate Z _{z , and the total cumulative number of passes P 2,2} = 1 is stored. Further, in the state 707 (X _q = X ₂ = 1.2, Z _z = Z ₃ = 1.2), the cumulative number of passes P _t = P (X ₃ , Z ₃ ) = 2 is the monthly interest rate X _q . It is added to the total cumulative number of passes P _{q, z} (initial value 0) for a pair of approximate cumulative average interest rates Z _{z , and the total cumulative number of passes P 3,3} = 2 is stored.

Instead of transitioning from the state 705 containing the cumulative average interest rate Y _{q to the state 707 containing the approximate average interest rate Z z} by approximation, from the cumulative average interest rate Y _q to the two closest approximate average interest rates Z _z-1 and Z _z. The cumulative number of paths P _t may be approximately proportionally distributed to the two states 708 and 709 according to the distance of. For example, for the cumulative average interest rate Y ₃ = 1.15, the cumulative number of passes for the state 708 (Z ₂ = 1.1) and the state 709 (Z ₃ = 1.2) for the current month interest rate X _{3 = 1.2.} Each pass number 1 of P (X ₃ , Y _{3 ) = 2 may be distributed and added to the total cumulative pass numbers P 3,2} = 1 and P _3,3 = 1 (Fig. 7A, dashed line). ..

In FIG. 7B, referring to the interest rate transition frequency table 700 (FIG. 4C), the monthly interest rate X ₂ = 1.1 (transition frequency 1 _{) from the state 706 (X 2 = 1.1) in the next month t = 2.} ) State 712 and _{the state 714 of monthly interest rate X 3} = 1.2 (transition frequency 2) are obtained.

In state 712, the cumulative average interest rate Y _q for the current month interest rate X ₂ = 1.1 for the month t = 2 is Y _q = Y ₂ = (Z) from the approximate average interest rate Z _{z for} the previous month t = 1 and the monthly interest rate X _{q. It is calculated as 2} × t + X ₂ ) / (t + 1) = (1.1 × 2 + 1.1) / 3 = 1.1. In addition, the cumulative number of passes P _t = P (X ₂ , Y ₂ ) for the current month interest rate X ₂ and the cumulative average interest rate Y ₂ is the total cumulative number of passes P ₁ = P _{2, 2} = 1 for the month t = 1, and the month. It is the product of the transition frequency 1 from the interest rate X ₂ to the monthly interest rate X _{2 , and is calculated as P 2} = P ₁ × T (X ₂ , X ₂ ) = 1 × 1 = 1.

In state 714, the cumulative average interest rate Y _q for the current month interest rate X ₃ = 1.2 for the month t = 2 is Y _q = Y ₂ = (Z) from the approximate average interest rate Z _{z for} the previous month t = 1 and the monthly interest rate X _{q. It is calculated as 2} × t + X ₃ ) / (t + 1) = (1.1 × 2 + 1.2) /3≈1.133. In addition, the cumulative number of passes P ₂ = P (X ₃ , Y ₂ ) for the current month interest rate X ₃ and the cumulative average interest rate Y ₃ is the total cumulative number of passes P ₁ = P _{2, 2} = 1 for the month t = 1, and the month. It is the product of the transition frequency ₂ from the interest rate X 2 to the monthly interest rate X _{3 , and is calculated as P 2} = P ₁ × T (X ₂ , X ₃ ) = 1 × 2 = 2.

The states 712 and 714 then transition by approximation to states 732 and 736 containing the approximate mean interest rate Z _z closest to each cumulative mean interest rate Y _{q at each interest rate X q, respectively.} In this case, in the state 732 (X _q = X ₂ = 1.1, Z _z = Z ₂ = 1.1), the cumulative number of passes P _t = P (X ₂ , Y ₂ ) = 1 is the monthly interest rate X _q. Is added to the total cumulative number of paths P _{q, z} (initial value 0) for a pair of approximate average interest rates Z _{z , and P 3,3} = 2 is stored. Further, in the state 736 (X _q = X ₃ = 1.2, Z _z = Z ₂ = 1.1), the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 2 is the monthly interest rate X _q . It is added to the total cumulative number of paths P _{q, z} (initial value 0) for a pair of approximate average interest rates Z _{z , and P 3,3} = 2 is stored.

Next, referring to the interest rate transition frequency table 700 (Fig. 4C) again, from the state 707 (previous month interest rate X ₃ = 1.2) to the state 716 of the monthly interest rate X ₂ = 1.1 (transition frequency 1). A state 718 with a monthly interest rate X ₃ = 1.2 (transition frequency 1) and _{a state 720 with a monthly interest rate X 4} = 1.3 (transition frequency 1) are obtained.

In state 716, the cumulative average interest rate Y _q for the current month interest rate X ₂ = 1.1 for the month t = 2 is Y _q = Y ₃ = (Z) from the approximate average interest rate Z _{z for} the previous month t = 1 and the monthly interest rate X _{q. It is calculated as 3} × t + X ₂ ) / (t + 1) = (1.2 × 2 + 1.1) / 3 = 1.166. In addition, the cumulative number of passes P _t = P (X ₂ , Y ₃ ) for the current month interest rate X ₂ and the cumulative average interest rate Y ₂ is the total cumulative number of passes P ₁ = P _3,3 = 2 for the month t = 1, and the previous month. It is the product of the transition frequency 1 from the interest rate X ₃ to the current month interest rate X _{2 , and is calculated as P 2} = P ₁ × T (X ₃ , X ₂ ) = 2 × 1 = 2.

In state 718, the cumulative average interest rate Y _q for the current month interest rate X ₃ = 1.2 is Y _q = Y ₃ = (Z ₃ × t + X ₃ ) _{from the approximate average interest rate Z z} of the previous month t = 1 and the current month interest rate X _q. It is calculated as / (t + 1) = (1.2 × 2 + 1.2) /3=1.2. In addition, the cumulative number of passes P _t = P (X ₃ , Y ₃ ) for the current month interest rate X ₃ and the cumulative average interest rate Y ₃ = 1.2 is the total cumulative number of passes P ₁ = P _{3, 3} = for the month t = 1. It is the product of ₂ and the transition frequency 1 from the previous month's interest rate X ₃ to the current month's interest rate X ₃ , and is calculated as P 2 = P _3,3 × T (X ₃ , X ₃ ) = 2 × 1 = 2.

In state 720, the cumulative average interest rate Y _q for the current month interest rate X ₄ = 1.3 is Y _q = Y ₄ = (Z ₃ × t + X ₄ ) _{from the approximate average interest rate Z z} of the previous month t = 1 and the current month interest rate X _q. / (T + 1) = (1.2 × 2 + 1.3) /3≈1.233. In addition, the cumulative number of paths P _t = P (X ₄ , Y ₄ ) for the current month interest rate X ₄ = 1.3 and the cumulative average interest rate Y ₄ = 1.233 is the total cumulative number of paths P ₁ = P for the month t = 1. It is the product of _3,3 = 2 and the transition frequency 1 from the previous month's interest rate X ₃ to the current month's interest rate X _{4 , and P 2} = P _3,3 × T (X ₃ , X ₄ ) = 2 × 1 = 2. Calculated.

The states 716, 718 and 720 then transition by approximation to states 734, 738 and 740 containing the approximate mean interest rate Z _z closest to each cumulative mean interest rate Y _{q at each interest rate X q.} In this case, in the state 734 (X _q = X ₂ = 1.1, Z _z = Z ₃ = 1.2), the cumulative number of passes P _t = P (X ₂ , Z ₂ ) = 2 is the monthly interest rate X _q. Is added to the total cumulative number of paths P _{q, z} (initial value 0) for a pair of approximate average interest rates Z _{z , and P 2,3} = 2 is stored. Further, in the state 738 (X _q = X ₃ = 1.2, Z _z = Z ₃ = 1.2), the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 2 is the monthly interest rate X _q . It is added to the total cumulative number of paths P _{q, z} (initial value 0) for a pair of approximate average interest rates Z _{z , and P 3,3} = 2 is stored. Further, in the state 740 (X _q = X ₄ = 1.3, Z _z = Z ₃ = 1.2), the cumulative number of passes P _t = P (X ₄ , Y ₄ ) = 2 is the monthly interest rate X _q . It is added to the total cumulative number of paths P _{q, z} (initial value 0) for a pair of approximate average interest rates Z _{z , and P 4,3} = 2 is stored.

In FIG. 7C, referring to the interest rate transition frequency table 700 (FIG. 4C), in the next month t = 3, from the state 732 (X ₂ = 1.1), the monthly interest rate X ₂ = 1.1 (transition frequency 1). ) State 752 and _{the state 754 of monthly interest rate X 3} = 1.2 (transition frequency 2) are obtained. Then, in the state 752, as in the state 712 of FIG. 7B, the monthly interest rate X ₂ = 1.1, the cumulative average interest rate Y ₂ = 1.1, and the cumulative number of passes P _t = P (X ₂ , Y ₂ ) = 1. × 1 = 1 is obtained. Similarly, in the state 754, the monthly interest rate X ₃ = 1.2, the cumulative average interest rate Y ₂ = 1.125, and the cumulative number of passes P _t = P (X ₃ , Y ₂ ) = 1 × 2 = 1 are obtained. Be done. The states 752 and 754 then transition to each state 782 (X ₂ = 1.1, Z ₂ = 1.1) and state 786 (X ₃ = 1.2, Z ₂ = 1.1) by approximation. do. In the state 782, the cumulative number of passes P _t = P (X ₂ , Y ₂ ) = 1 becomes the total cumulative number of passes P _{q, z} (initial value 0) for a _{pair of the monthly interest rate X q} and the approximate average interest rate Z _z. It is added and P _2,2 = 1 is saved. In the state 786, the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 2 becomes the total cumulative number of passes P _{q, z} (initial value 0) for a _{pair of the monthly interest rate X q} and the approximate average interest rate Z _z. It is added and P _3,2 = 2 is saved.

Similarly, referring to the interest rate transition frequency table 700 (Fig. 4C), in the month t = 3, the monthly interest rate X ₂ = 1.1 (transition frequency 1) _{from the previous month interest rate X 2 = 1.1 in the state 734.} A state 756 and a state 758 with a monthly interest rate X ₃ = 1.2 (transition frequency 2) are obtained. Similarly, in the state 756, the monthly interest rate X ₂ = 1.1, the cumulative average interest rate Y ₃ = 1.175, and the cumulative number of passes P _t = P (X ₂ , Y ₃ ) = 2 × 1 = 2 are obtained. Similarly, in the state 758, the monthly interest rate X ₃ = 1.2, the cumulative average interest rate Y ₃ = 1.2, and the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 2 × 2 = 4 are obtained. Be done. The states 756 and 758 then transition to states 784 (X ₂ = 1.1, Z ₃ = 1.2) and states 788 (X ₃ = 1.2, Z ₃ = 1.2) by approximation. .. In the state 784, the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 2 becomes the total cumulative number of passes P _{q, z} (initial value 0) for a _{pair of the monthly interest rate X q} and the approximate average interest rate Z _z. It is added and P _2,3 = 2 is saved. In the state 788, the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 4 becomes the total cumulative number of passes P _{q, z} (initial value 0) for a _{pair of the monthly interest rate X q} and the approximate average interest rate Z _z. It is added and P _3,3 = 4 is saved.

Similarly, in the month t = 3, the previous month interest rate X ₂ = 1.2 _{in the state 736, the state 760 in the monthly interest rate X 2} = 1.1 (transition frequency 1), and the monthly interest rate X ₃ = 1.2 (transition). The state 762 of the _{frequency 1) and the state 764 of the monthly interest rate X 4} = 1.3 (transition frequency 1) are obtained. Similarly, in the state 760, the monthly interest rate X ₂ = 1.1, the cumulative average interest rate Y ₂ = 1.1, and the cumulative number of passes P _t = P (X ₂ , Y ₂ ) = 2 × 1 = 2 are obtained. Similarly, in the state 762, the monthly interest rate X ₃ = 1.2, the cumulative average interest rate Y ₃ = 1.125, and the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 2 × 1 = 2 are obtained. Be done. Similarly, in the state 764, the monthly interest rate X ₄ = 1.3, the cumulative average interest rate Y ₃ = 1.15, and the cumulative number of passes P _t = P (X ₄ , Y ₃ ) = 2 × 1 = 2 are obtained. Be done. The states 760, 762 and 764 are then approximated to state 782 (X ₂ = 1.1, Z ₂ = 1.1), state 786 (X ₃ = 1.2, Z ₂ = 1.1). The state transitions to the state 790 (X ₄ = 1.3, Z ₃ = 1.2). In the state 782, the cumulative number of passes P _t = P (X ₂ , Y ₂ ) = 2 becomes the total cumulative number of passes P _{q, z} (current value 1) for a _{pair of the monthly interest rate X q} and the approximate mean interest rate Z _z. It is added and P _2,2 = 3 is saved. In the state 786, the cumulative number of passes P _t = P (X ₂ , Y ₂ ) = 2 becomes the total cumulative number of passes P _{q, z} (current value 2) for a _{pair of the monthly interest rate X q} and the approximate mean interest rate Z _z. It is added and P _3,2 = 4 is saved. In the state 790, the cumulative number of passes P _t = P (X ₄ , Y ₃ ) = 2 becomes the total cumulative number of passes P _{q, z} (initial value 0) for a _{pair of the monthly interest rate X q} and the approximate average interest rate Z _z. It is added and P _4,3 = 2 is saved.

Similarly, at monthly t = 3, the previous month interest rate X ₂ = 1.2 _{in the state 738, the state 766 in the monthly interest rate X 2} = 1.1 (transition frequency 1), and the monthly interest rate X ₃ = 1.2 (transition). The state 768 of the _{frequency 1) and the state 770 of the monthly interest rate X 4} = 1.3 (transition frequency 1) are obtained. Similarly, in the state 766, the monthly interest rate X ₂ = 1.1, the cumulative average interest rate Y ₃ = 1.175, and the cumulative number of passes P _t = P (X ₂ , Y ₃ ) = 2 × 1 = 2. Similarly, in the state 768, the monthly interest rate X ₃ = 1.2, the cumulative average interest rate Y ₃ = 1.2, and the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 2 × 1 = 2 are obtained. Be done. Similarly, in the state 770, the monthly interest rate X ₄ = 1.3, the cumulative average interest rate Y ₂ = 1.225, and the cumulative number of passes P _t = P (X ₄ , Y ₃ ) = 2 × 1 = 2 are obtained. Be done. The states 766, 768 and 770 are then approximated to the states 784 (X ₂ = 1.1, Z ₃ = 1.2), the state 788 (X ₃ = 1.2, Z ₃ = 1.2). Each transitions to the state 790 (X ₄ = 1.3, Z _{3 = 1.2).} In the state 784, the cumulative number of passes P _t = P (X ₂ , Y ₃ ) = 2 becomes the total cumulative number of passes P _{q, z} (current value 2) for a _{pair of the monthly interest rate X q} and the approximate mean interest rate Z _z. It is added and P _2,2 = 4 is saved. In the state 788, the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 2 becomes the total cumulative number of passes P _{q, z} (current value 4) for a _{pair of the monthly interest rate X q} and the approximate mean interest rate Z _z. It is added and P _3,3 = 6 is saved. In the state 790, the cumulative number of passes P _t = P (X ₄ , Y ₃ ) = 2 becomes the total cumulative number of passes P _{q, z} (current value 2) for a _{pair of the monthly interest rate X q} and the approximate mean interest rate Z _z. It is added and P _4,3 = 4 is saved.

Similarly, at the month t = 3, the state 772 of the monthly interest rate X ₃ = 1.2 (transition frequency 1) is obtained _{from the previous month interest rate X 4 = 1.3 of the state 740.} Similarly, in the state 772, the monthly interest rate X ₃ = 1.2, the cumulative average interest rate Y ₃ = 1.2, and the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 2 × 1 = 2 are obtained. The state 772 then transitions to the state 788 (X ₃ = 1.2, Z ₃ = 1.2) by approximation. In the state 788, the cumulative number of passes P _t = P (X ₃ , Y ₃ ) = 2 becomes the total cumulative number of passes P _{q, z} (current value 6) for a _{pair of the monthly interest rate X q} and the approximate mean interest rate Z _z. It is added and P _3,3 = 8 is saved.

After that, the same process is repeated from the next current month t = 4 to the last current month t = M. In this way, the total cumulative transition paths of interest rate transitions from the initial interest rate to each approximate average interest rate can be obtained.

FIG. 6A is a process executed by the information processing apparatus 10 for generating a table of interest rate transition frequencies (eg, FIGS. 4C, 5C) from a plurality of interest rates (eg, FIGS. 4A, 5A) over a series of past periods. An example of the flowchart of is shown.

Referring to FIG. 6A, in step 602, the processor 102 of the information processing apparatus 10 (or its interest rate transition frequency generation unit 1028) follows a user's operation with a series of past monthly interest rate data (eg, FIGS. 4A and 5A). Is read. In step 604, processor 102 (element 1028) sorts past monthly interest rate data in chronological order to generate past monthly interest rate data (eg, FIGS. 4A, 5A), with each month interest rate and next month interest rate. Pairs (X _p , X _q ) are generated as past monthly interest rate transition data (eg, FIGS. 4B and 5B) and stored in the storage unit 104.

In step 606, processor 102 (element 1028) has an unprocessed pair of interest rates consisting of a monthly interest rate and a next month interest rate in the record of past monthly interest rate transitions (eg, FIGS. 4B, 5B). To judge. If it is determined that there is no unprocessed pair of interest rates, the procedure exits the flowchart of FIG. 6A and proceeds to step 622 of FIG. 6B. If it is determined that there is a pair of unprocessed interest rates, in step 608, processor 102 (element 1028) reads out a _{pair of unprocessed interest rates (X p} , X _{q). In step 610, processor 102 (element 1028) determines if the same pair of interest rates (X p} , X _q ) is present in the interest rate transition frequency table (eg, FIGS. 4C, 5C). If it is determined that the same pair of interest rates exists, the procedure proceeds to step 614. If it is determined that the same pair of interest rates does not exist, in step 612, the processor 102 (element 1028) generates a record of the pair of interest rate transition frequencies and sets the transition frequency T to a value of 0 (initial value). Set to. The procedure then proceeds to step 612.

In step 614, the processor 102 (element 1028) increments the corresponding pair of interest rate transition frequencies T in the interest rate transition frequency record to set T = T + 1, that is, adds 1 to T. The procedure then returns to step 606. In this way, a table (eg, FIGS. 4C, 5C) consisting of records of a plurality of interest rate transition frequencies is generated from the past monthly interest rate transitions (eg, FIGS. 4B, 5B).

6B and 6C show the possible cumulative paths and forecast occurrences of each average interest rate for the period months M in the last month of months M starting _{at the initial monthly interest rate X 0} , after the flowchart of FIG. 6A. An example of a flowchart of the process for obtaining the ratio is shown.

Referring to FIG. 6B, in step 622, the processor 102 (or its condition setting unit 1026) displays a table of interest rate transition frequencies (eg, FIGS. 4C and 5C), period months M, and initial interest rate X _{0 from the storage unit 104.} Read. The number of months M and the initial interest rate X ₀ are values set or selected by the user. In step 624, the processor 102 (element 1026) sets _{t in the table of monthly interest rate (X q} ) / approximate average interest rate (Z _z ) / total cumulative number of passes (P _{q, z} ) (eg, FIG. 8A). Set as the initial value t = 0, current month interest rate X _q = X ₀ (X ₀ ∈ {x ₁ , x ₂ , ..., x _N }), approximate cumulative average interest rate Z _z = Z ₀ = X ₀ , approximate Set the total cumulative transition path number P _{q, z} = P ₀ = 1 (initial value) of the cumulative average interest rate Z _z = Z _0. As a result, an initial table (eg, FIG. 8A) of monthly interest rate / approximate average interest rate / total cumulative number of passes for the initial month t = 0 is generated.

In step 626, the processor 102 (or its cumulative number of paths calculation unit 1029) sets t for the current month. The first month t (= t + 1) is 1. In step 628, the processor 102 (element 1029) determines whether or not the current month t is the number of months M or less (t ≦ M). If it is determined that the current month t is the number of months M or less, the procedure proceeds to step 632 of FIG. If it is determined that the current month t is not less than or equal to the number of months M or exceeds the number of months M, the procedure proceeds to step 660.

Referring to FIG. 6C, in step 632, processor 102 (element 1029) determines if there _{is an unprocessed previous month interest rate X p in} the table of monthly interest rate / approximate average interest rate / total cumulative number of passes. Initially, X _p = X ₀ . Initially, there is an unprocessed X ₀ . If it is determined that there is an unprocessed previous month interest rate X _{p in} the table, in step 634, the processor 102 (element 1029) has the monthly interest rate / approximate average interest rate / total cumulative path of the previous month t-1 in the table. Refer to a number of outstanding records (rows).

In step 636, the processor 102 (element 1029) reads the interest rate X q of each transition destination _{to the unprocessed previous month interest rate X p} with reference to the interest rate transition frequency table (eg, FIGS. 4C and 5C), and reads the previous _{month interest rate X q.} Generate a working record of interest rate / approximate average interest rate / current month interest rate (eg, 803 in FIG. 8B).

In step 638, processor 102 (element 1029) calculates the current month's cumulative average interest rate Y _q and the cumulative number of transition paths P _t (X _q , Y _q ) for the _{current month interest rate X q in each generated work record.} Determine the approximate cumulative average interest rate Z _z. The cumulative number of transition paths P _t (X _q , Y _q ) for the current month interest rate X _q is the cumulative number of transition paths P _t-1 of the previous month t-1 and the transition frequency T (transition frequency T from the previous month interest rate X _p to the current month interest rate X _q). X _p, the product _{P t-1 × T (X} p and X _q), is determined as X _q). Month cumulative average rate Y _q relates month rate X _q, the sum of the product and month interest X _q previous month t-1 cumulative average rate Z _z from the previous month t-1 to the number of months (t), current month month It is a value divided by a few tons. The processor 102 (element 1029) then receives an approximate cumulative average interest rate Z _z ∈ {x ₁ , x ₂ ,. .. .. , X _N }, the approximate cumulative average interest rate Z _z closest to the cumulative average interest rate Y _q of the current month t is determined as the approximate value of the cumulative average interest rate Y _{q of the current month.} The number of approximate cumulative average rate Z _z to be determined may be one or two. When the number of approximate cumulative average interest rates Z _z is 2, the cumulative transition path number P _t (X _q , Y _q ) is distributed to two approximate cumulative average interest rates Z _z according to the difference from the cumulative average interest rate Y _q. May be done.

In step 640, the processor 102 (element 1029) sets the total cumulative transition paths P _{q, z} of the current month interest rate X _{q with respect to the obtained approximate cumulative average interest rate Z z} in the table of monthly interest rate / approximate average interest rate / cumulative number of paths. Add the cumulative number of transition paths P _t. In this way, a table of monthly interest rate / approximate average interest rate / cumulative number of passes is generated (eg, 804 in FIG. 8B). The procedure then returns to step 632. If it is determined in step 632 that there is no unprocessed previous month interest rate X _p in the table, the procedure returns to step 626 of FIG. 6B.

If it is determined in step 628 of FIG. 6B that the current month t is not less than or equal to the number of months M, that is, the current month t exceeds the number of months M, in step 660, the processor 102 (element 1029) determines each approximate cumulative average interest rate. The total of the total cumulative transition paths P _{q and z for Z z} and the predicted occurrence rate thereof are calculated and displayed (eg, FIG. 8G).

Next, according to the flowcharts of FIGS. 6B and 6C, the approximate cumulative average interest rate and the cumulative transition path number are used using the monthly interest rate / approximate average interest rate / cumulative pass number table and the previous month interest rate / approximate average interest rate / current month interest rate work record. An example of a procedure for determining the rate of occurrence of a combination will be described.

8A-8G show the approximate cumulative average interest rate and the cumulative transition using the monthly interest rate / approximate average interest rate / cumulative number of passes table and the previous month interest rate / approximate average interest rate / current month interest rate work record according to the flowcharts of FIGS. 6B and 6C. An example of the procedure for determining the occurrence rate of the combination of the number of passes is shown.

In FIG. 8A, in the initial table 801 of the monthly interest rate / approximate average interest rate / cumulative number of passes, the current month interest rate X _q = X ₀ = 1.1% and the approximate cumulative average interest rate Z _z = Z at the initial month t = 0. ₀ = 1.1% and the total cumulative number of transition paths P _{q, z} = P ₀ (X ₀ , Z ₀ ) = 1 are initially set.

Referring to FIG. 8B, assuming that the current month t = 1, the work record 803 of the previous month interest rate / approximate average interest rate / current month interest rate includes the item (field) of the previous month t-1 and the item of the current month t of the transition destination. In the work record 803, according to the interest rate transition frequency table of FIG. 4C, the previous month interest rate X _p = 1.1% has two current month interest rates of 1.1% and 1.2% at the transition destination, and therefore two records ( 2 lines) are generated. In the first record, in the item of the previous month t-1, from the initial table 801 of FIG. 8A, the previous month interest rate X _p = 1.1%, the approximate cumulative average interest rate Z _z = 1.1%, and the cumulative number of transition paths P _{t. -1 = 1 is copied and stored, and the current month interest rate X q} = 1.1% and the transition frequency T (X _p , X _q ) = 1 are copied from the interest rate transition frequency table in Fig. 4C to the item of the current month t. Is stored. In the second record, in the item of t-1 of the previous month, from the initial table 801, the interest rate of the previous month X _p = 1.1%, the approximate cumulative average interest rate Z _z = 1.1%, and the number of cumulative transition paths P _t-1 =. _{1 is copied and stored, and the current month interest rate X q} = 1.2% and the transition frequency 2 are copied and stored in the item of the current month t from the interest rate transition frequency table of FIG. 4C.

Next, in the first record, the cumulative number of transition paths P _{t of the current month t is the cumulative number of transition paths P t-1} = (X _p , Z _z ) = 1 of the previous month t-1, and the transition frequency T (X _p , X _q ) = 1 is multiplied to obtain P _t = 1. Next, as described with respect to the state 704 in FIG. 7A, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.100% by the monthly weighted average of the cumulative average interest rate Z _z and the interest rate for the current month. Next, the approximate average interest rate Z _z = 1.1%, which is the closest to the cumulative interest rate Y _{q = 1.100% for the current month, is determined.} Next, in the second record, the cumulative number of transition paths P _{t of the current month t is the cumulative number of transition paths P t-1} = (X _p , Z _z ) = 1 of the previous month t-1, and the transition frequency T (X _p , X _q ) = 2 is multiplied to obtain P _t = 2. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.150% by the monthly weighted average of the cumulative average interest rate Z _z and the interest rate for the current month, as described above. Next, the approximate average interest rate Z _z = 1.2, which is the closest to the cumulative interest rate Y _{q = 1.150% for the current month, is determined.} In this case, rounding is applied.

Next, in Table 804 of monthly interest rate / approximate average interest rate / cumulative number of passes, two records _{regarding the approximate average interest rate Z z} = 1.1 and 1.2 in the first and second records of the work record 803 are generated. To. In Table 804, the current month interest rate Z _q = 1.1 and the approximate average interest rate Z _z = 1.1 are copied and stored in the first record from the work record 803, and the total cumulative transition paths P _{q, z} (initial). The cumulative number of transition paths P _t = 1 is added to the value 0). Further, in Table 804, the current month interest rate X _q = 1.2 and the approximate average interest rate Z _z = 1.2 are copied and stored in the second record from the work record 803, and the total cumulative transition paths P _{q, z are stored.} The cumulative number of transition paths P _t = 2 is added to (initial value 0). In this way, a table 804 of monthly interest rate / approximate average interest rate / cumulative number of passes for monthly t = 1 is generated.

Referring to FIG. 8C, the work record 806 of the current month t = 2 is set as in FIG. 8B. In the work record 806 of FIG. 8C, two records (two rows) are generated for _{the previous month interest rate X p} = 1.1% according to the table of interest rate transition frequency of FIG. 4C, as in the case of FIG. 8B. In the first record, in the item of t-1 of the previous month, from Table 804 of FIG. 8B, the interest rate of the previous month X _p = 1.1%, the approximate average interest rate Z _z = 1.1%, and the cumulative number of passes P _t-1 = 1. _{Is copied and stored, and the current month interest rate X q} = 1.1% and the transition frequency T (X _p , X _q ) = 1 are copied and stored in the item of the current month t from the table of interest rate transition frequency in FIG. 4C. To. In the second record, in the item of t-1 of the previous month, from Table 804 of FIG. 8B, the interest rate of the previous month X _p = 1.1%, the approximate average interest rate Z _z = 1.1%, and the cumulative number of passes P _t-1 = 1. _{Is copied and stored, and the current month interest rate X q} = 1.2% and the transition frequency 2 are copied and stored in the item of the current month t from the interest rate transition frequency table of FIG. 4C.

Next, in the first record, the cumulative number of passes P _{t for the current month t is calculated as P t} = 1 as described above. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.100 as described above. Next, the approximate average interest rate Z _z = 1.1, which is the closest to the cumulative interest rate Y _{q = 1.100 for the current month, is determined.} Next, in the second record, the cumulative number of passes P _{t for the current month t is calculated as P t} = 2 as described above. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.133 as described above. Next, the approximate average interest rate Z _z = 1.1, which is the closest to the cumulative interest rate Y _{q = 1.133 for the current month, is determined.}

Further, in the work record 806, three more records (three rows) are _{similarly generated for the previous month interest rate X p} = 1.2 according to the interest rate transition frequency table of FIG. 4C. _{In the third record, the previous month interest rate X p} = 1.2, the approximate average interest rate Z _z = 1.2, and the cumulative number of passes P _t-1 = 2 are copied from Table 804 in FIG. 8B to the item of the previous month t-1. _{The current month interest rate X q} = 1.1 and the transition frequency T (X _p , X _q ) = 1 are copied and stored in the item of the current month t from the interest rate transition frequency table of FIG. 4C. _{In the fourth record, the previous month interest rate X p} = 1.2, the approximate average interest rate Z _z = 1.2, and the cumulative number of passes P _t-1 = 2 are copied from Table 804 in FIG. 8B to the item of the previous month t-1. _{The current month interest rate X q} = 1.2 and the transition frequency 1 are copied and stored in the item of the current month t from the interest rate transition frequency table of FIG. 4C. _{In the fifth record, the previous month interest rate X p} = 1.2, the approximate average interest rate Z _z = 1.2, and the cumulative number of passes P _t-1 = 2 are copied from Table 804 in FIG. 8B to the item of the previous month t-1. _{And stored, the current month interest rate X q} = 1.3 and the transition frequency 1 are copied and stored in the item of the current month t from the table of interest rate transition frequency in FIG. 4C.

Next, in the third record, the cumulative number of passes P _{t for the current month t is calculated as P t} = 2 as described above. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.166 as described above. Next, the approximate average interest rate Z _z = 1.2, which is the closest to the cumulative interest rate Y _{q = 1.166 for the current month, is determined.} Next, in the fourth record, the cumulative number of passes P _{t for the current month t is calculated as P t} = 2 as described above. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.200 as described above. Next, the approximate average interest rate Z _z = 1.2, which is the closest to the cumulative interest rate Y _{q = 1.200 for the current month, is determined.} Next, in the fifth record, the cumulative number of passes P _{t for the current month t is calculated as P t} = 2 as described above. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.233 as described above. Next, the approximate average interest rate Z _z = 1.2, which is the closest to the cumulative interest rate Y _{q = 1.233 for the current month, is determined.}

Next, in Table 807 of monthly interest rate / approximate average interest rate / cumulative number of passes, five records _{relating to the approximate average interest rate Z z} = 1.1 and 1.2 in the first to fifth records of the work record 806 are generated. To. In Table 807, the first and second records are generated from the working record 806 in the same manner as in FIG. 8B. In Table 807, the current month interest rate Z _q = 1.1 and the approximate average interest rate Z _z = 1.2 are copied and stored in the third record from the work record 803, and the total cumulative number of paths P _{q, z} (initial value). The cumulative number of passes P _t = 2 is added to 0). Further, in Table 807, the current month interest rate Z _q = 1.2 and the approximate average interest rate Z _z = 1.2 are copied and stored in the fourth record from the work record 806, and the total cumulative number of paths P _{q, z} ( The cumulative number of passes P _t = 2 is added to the initial value 0). Further, in Table 807, the current month interest rate Z _q = 1.3 and the approximate average interest rate Z _z = 1.2 are copied and stored in the fifth record from the work record 806, and the total cumulative number of paths P _{q, z} ( The cumulative number of passes P _t = 2 is added to the initial value 0). In this way, the table 807 of the monthly interest rate / approximate average interest rate / cumulative number of passes for the month t = 2 is generated.

Referring to FIG. 8D, the form of the work record 809 of the current month t = 3 is similarly set. In the work record 809 of FIG. 8D, 11 records (11 rows) are _{similarly generated for the previous month interest rates X p} = 1.1, 1.2 and 1.3 according to the interest rate transition frequency table of FIG. 4C. .. Similarly, the work record 809 of the previous month interest rate / approximate average interest rate / current month interest rate of FIG. 8D is generated. Next, in Table 810 of monthly interest rate / approximate average interest rate / cumulative number of passes, five records _{relating to the approximate average interest rate Z z} = 1.1 and 1.2 in the first to fifth records of the work record 809 are generated. To. In Table 810, the current month interest rate Z _q = 1.1 and the approximate average interest rate Z _z = 1.1 in the work record 809 are copied and stored in the first record, and the total cumulative number of paths P _{q, z} (initial). The cumulative number of passes P _t = 1 is added to the value 0). Further, in Table 810, the next current month interest rate X _q = 1.1 and the approximate average interest rate Z _z = 1.1 in the work record 809 are identified, and the total cumulative number of passes of the first record P _{q, z} ( The cumulative number of passes P _t = 2 is added to the current value 1). Further, in Table 810, the current month interest rate X _q = 1.2 and the approximate average interest rate Z _z = 1.1 in the work record 809 are copied and stored in the second record, and the total cumulative number of paths P _{q, z is stored.} The cumulative number of passes P _t = 2 is added to (initial value 0). Further, in Table 810, the next current month interest rate X _q = 1.2 and the approximate average interest rate Z _z = 1.1 in the work record 809 are identified, and the total cumulative number of passes of the second record P _{q, z} ( The cumulative number of passes P _t = 2 is added to the current value 2).

In this way, the total cumulative number of passes P _{q, z} is generated for each pair of the current month interest rate X _q and the approximate mean interest rate Z _z. In this way, the table 810 of the monthly interest rate / approximate average interest rate / cumulative number of passes for the month t = 3 is generated.

Referring to FIG. 8E, the form of the work record 812 of the current month t = 4 is similarly set. In the work record 812 of FIG. 8E, 11 records (11 rows) are _{similarly generated for the previous month interest rates X p} = 1.1, 1.2 and 1.3 according to the interest rate transition frequency table of FIG. 4C. .. Similarly, the work record 809 of the previous month interest rate / approximate average interest rate / current month interest rate of FIG. 8E is generated, and the table 813 of the monthly interest rate / approximate average interest rate / cumulative number of passes is generated.

With reference to FIG. 8F, the form of the work record 815 of the current month t = 5 is similarly set. In the work record 815 of FIG. 8F, 11 records (11 rows) are _{similarly generated for the previous month interest rates X p} = 1.1, 1.2 and 1.3 according to the interest rate transition frequency table of FIG. 4C. .. Similarly, the work record 815 of the previous month interest rate / approximate average interest rate / current month interest rate of FIG. 8F is generated, and the table 816 of the monthly interest rate / approximate average interest rate / cumulative number of passes is generated.

Figure 8G shows an example of a generation ratio of each approximate average interest Z _z to be displayed on the display unit 124 of the information processing apparatus 10. The processor 102 (element 1029) sums the total cumulative number of passes P _{q, z for each approximate average interest rate Z Z} in FIG. 8F for all current month interest rates X _q , and the cumulative number of passes P for each approximate average interest rate Z _z. Request _z (respectively P _q relative to _{Z z = 1.0,1.1,1.2,1.3, z = 0,51,98,0} ). Next, the processor 102 (element 1029) normalizes the cumulative number of passes P _{z of each approximate average interest rate Z z} so that the total total is 1, and obtains the predicted occurrence ratio of _{each approximate average interest rate Z z.} ( _{Occurrence rate = 0, 0.34, 0.66, 0 for Z z} = 1.0, 1.1, 1.2, 1.3, respectively). The processor 102 (element 1029) has an initial interest rate of X ₀ = 1.1%, a period of months M = 6 months, and an average interest rate of 1.1% and 1.2% on the display device 124, respectively. Display 0.34 and 0.66. In this case, the rate of occurrence of average interest rates of 1.0% and 1.3% is 0 (zero).

The user can determine the interest rate of the corporate bond based on the display information of FIG. 8G, the average interest rates of 1.1% and 1.2%, and the accrual rates of 0.34 and 0.66.

As mentioned above, when predicting the number of interest rate transition passes based on past interest rate experience data, when distributing the current month's cumulative average interest rate to the approximate average interest rate, and when allocating the cumulative number of passes to the total cumulative number of passes. , An approximation occurs. However, when the cumulative number of passes is assigned to the total cumulative number of passes, the number of passes is not rounded off, rounded down, or rounded up to the nearest whole number, so that the processing error is small.

Next, another embodiment in which the cumulative transition probability of the interest rate (hereinafter, also referred to as “cumulative probability”) is applied instead of the number of cumulative transition paths of the interest rate described above will be described.

_{FIG. 9A shows an example of the interest rate transition probability matrix Sp, q} generated according to the interest rate transition frequency table (experience data) of FIG. 4C. The interest rate transition probability matrix S _{p, q} is normalized so that the total of the transition probabilities from each of the _four interest rates x _{1 to x 4 to the three interest rates x 2 to x 4 in one row is 1.0.} There is. FIG. 9B shows an example of Table 900 of interest rate transition probabilities generated according to the interest rate transition frequency table of FIG. 4C. Table 900 interest transition probabilities are normalized such that the sum of the transition probabilities of the previous month interest x ₁ ~x next month transition from each of the ₄ one or more interest rate x ₂ ~x ₄ becomes 1.0 To. FIG. 9C shows an example of the interest rate transition probability matrix _{Sp, q} generated according to the interest rate transition frequency table of FIG. 5C. _{Similarly, in the} interest rate transition probability matrix Sp, q, the total of the transition probabilities from 9 interest rates 0.2 to 1.2% to 9 interest rates 0.2 to 1.2% in one row is 1. It is normalized to be 0. _{In the matrices Sp, q} of FIGS. 9A and 9C, the distribution of the probabilities near the diagonal positions is different from the generally applied normal distribution, and the transition probabilities of the diagonal positions may be 0.

When selecting or extracting past interest rates as in FIGS. 4A and 5A, it is preferable to select or extract so that the interest rate in the last period or month does not become the maximum or minimum interest rate in the entire period. The reason is that there is no transition destination from the maximum or minimum value of the interest rate to another interest rate.

_{FIG. 11 shows the interest rate X q of} each month from the pair _{of the initial interest rate X 0 of the} first month t = 0 and the initial cumulative average interest rate Z ₀ based on the interest rate transition probability table 900 of FIG. 9B according to the embodiment. And the transition of the cumulative average interest rate Y _q to one pair, and the transition or mapping of the _{interest rate X q} and the approximate cumulative average interest rate Z _{z to each pair are shown.}

Month cumulative transition probabilities interest rate X _q cumulative average rate Y _q in month _{t C t = C (X q} , Y q) is the previous month t-1 of interest X _p and the cumulative average rate Z _z about the cumulative transition probabilities C _t It is expressed by the following equation as the product of _-1 = C (X _p , Z _z ) and the transition probability S (X _p , X _{q ) from the interest rate X p} of the previous month t-1 to the interest _{rate X q of the} current month t. To.
C _t = C (X _q , Y _q ) = C _t-1 × S (X _p , X _q ) = C (X _p , Z _z ) × S (X _p , X _q )

In FIG. 11, in the initial state 902 of the first month t = 0, the initial interest rate is X ₀ = X ₂ = 1.1%, and the initial cumulative average interest rate is Z ₀ = X ₀ = 1.1%. The initial value of the cumulative transition probability for the initial interest rate X ₀ and the cumulative average interest rate Z _{0 is C 0} = C (X ₀ , Z ₀ ) = 1. For the initial interest rate X _{0 , the value of the previous month interest rate X p in} Table 900 of the interest rate transition probability in FIG. 9B is selected.

In the next month t = 1, referring to Table 900 (Fig. 9B) of interest rate transition probabilities, the current month interest rate X ₂ = 1.1% ( _{as the transition destination from the previous month interest rate X 2 = 1.1 in the initial state 902).} A state 904 with a transition probability of 0.33) and _{a state 905 with a current month interest rate X 3} = 1.2% (transition probability 0.67) can be obtained.

In state 904, the cumulative average interest rate Y _q for the current month interest rate X ₂ = 1.1% for the current month t = 1 is the cumulative average interest rate Z ₀ = 1.1% for the previous month t = 0 and the current month interest rate X _q = X ₂ =. From 1.1%, _{it is calculated as Y q} = Y ₂ = (1.1 × 1 + 1.1) / 2 = 1.1%. Further, the cumulative transition probability C _{t = 1} = C (X ₂ , Y ₂ ) from the initial state 902 to the state 904 (current month interest rate X ₂ = 1.1%, cumulative average interest rate Y ₂ = 1.1%) is. It is the product of the total cumulative transition probability C _{q, z} = C ₀ = 1 of the month t = 0 and the transition probability S (X ₂ , X ₂ ) = 0.33 from the previous month interest rate X ₀ to the current month interest rate X _2. , P ₀ × T (X ₂ , X ₂ ) = 1 × 0.33 = 0.33. The total cumulative transition probability is also hereinafter referred to as “total cumulative probability”.

In state 705, the cumulative average interest rate Y _q for the current month interest rate X ₃ = 1.2 for the current month t = 1 is the cumulative average interest rate Z ₀ = 1.1 for the previous month t = 0 and the current month interest rate X _q = X ₃ = 1. From 2, _{it is calculated as Y q} = Y ₃ = (1.1 × 1 + 1.2) / 2 = 1.15. The cumulative transition probability C _{t = 1} = C ₁ (X ₃ , Y ₃ ) from the initial state 902 to the state 902 (X ₃ = 1.2, Y ₃ = 1.15) is the sum of the months t = 0. It is the product of the cumulative probability C _{q, z} = C ₀ = 1 and the transition probability S (X ₂ , X ₃ ) = 0.67 from the previous month's interest rate X ₀ to the current month's interest rate X _{3 , and is C 0} × S (X). ₂ , X ₃ ) = 1 x 0.67 = 0.67.

The states 904 and 905 are then transitioned or mapped by approximation to states 906 and 907 containing the approximate cumulative average interest rate Z _z closest to each cumulative average interest rate Y _{q at each interest rate X q, respectively.}

In the state 906 (X _q = X ₂ = 1.1, Z _z = Z ₂ = 1.1), the cumulative probability C _t = C (X ₂ , Y ₂ ) = 0.33 is close to the _{monthly interest rate X q.} It is added to the total cumulative probability C _{q, z} (initial value 0) for a pair of cumulative average interest rates Z _{z , and the total cumulative probability C 2,2} = 0.33 is stored. Further, in the state 907 (X _q = X ₂ = 1.2, Z _z = Z ₃ = 1.2), the cumulative probability C _t = C (X ₃ , Z ₃ ) = 0.67 is the monthly interest rate X _q. Is added to the total cumulative probability C _{q, z} (initial value 0) for a pair of the approximate cumulative average interest rate Z _{z , and the total cumulative probability C 3,3} = 0.67 is stored.

The states 904 and 905 are then transitioned or mapped by approximation to states 906 and 907 containing the approximate cumulative average interest rate Z _z closest to each cumulative average interest rate Y _{q at each interest rate X q, respectively.} Alternatively, the cumulative probability C _t can be approximately proportionally distributed to the two states 708 and 909 according to the distance from the cumulative mean interest rate Y _q to the two closest approximate mean interest rates Z _z-1 and Z _z. good. For example, for the cumulative average interest rate Y ₃ = 1.15, the cumulative probability C for the state 908 (Z ₂ = 1.1) and the state 909 (Z ₃ = 1.2) for the current month interest rate X _{3 = 1.2.} (X ₃ , Y ₃ ) = 0.67 _{may be distributed and added to the cumulative probabilities C 3,2} = 0.33 and C _3,3 = 0.34 (Fig. 11, dashed line).

In this way, the same process is repeated from t = 0 of the current month to t = M of the last month. In this way, the predicted probability of occurrence of each average interest rate can be obtained from the initial interest rate.

10A and 10B generate an interest rate transition probability after the flowchart of FIG. 6A, and predict each average interest rate of the period month M in the final month of the month number M starting from _{the initial monthly interest rate X 0.} An example of a flowchart of the process for obtaining the occurrence probability is shown.

Referring to FIG. 10A, in step 620, processor 102 (or its interest rate transition probability generator 1030) normalizes the interest rate transition frequency table (eg, FIGS. 4C and 5C) generated in FIG. 6A for each previous month's interest rate. To generate an interest rate transition probability matrix or a table of interest rate transition probabilities (eg, FIGS. 9A-9C).

In step 822, the processor 102 (or its condition setting unit 1026) reads a matrix or table of interest rate transition probabilities (eg, FIGS. 9A-9C), period months M, and initial interest rate X _{0 from the storage unit 104.} In step 824, the processor 102 (element 1031) initially sets t in the current month t in the table of _{monthly interest rate (X q} ) / approximate average interest rate (Z _z ) / total cumulative probability (C _{q, z) (eg, FIG. 12A).} Set the value t = 0, current month interest rate X _q = X ₀ (X ₀ ∈ {x ₁ , x ₂ ..., x _N }), approximate cumulative average interest rate Z _z = Z ₀ = X ₀ , total cumulative Set the transition probability C _{q, z} = C ₀ = 1.0 (initial value). As a result, an initial table of monthly interest rate / approximate mean interest rate / total cumulative probability with initial month t = 0 (eg, FIG. 12A) is generated.

In step 826, the processor 102 (or its average interest rate probability calculation unit 1031) sets t = t + 1 for the next month. The first month t is t + 1 = 1. In step 828, the processor 102 (element 1031) determines whether or not the current month t is the number of months M or less (t ≦ M). If it is determined that the current month t is the number of months M or less, the procedure proceeds to step 832 of FIG. 10B. If it is determined that the current month t is not less than or equal to the number of months M or exceeds the number of months M, the procedure proceeds to step 860.

Referring to FIG. 10B, in step 832, processor 102 (element 1031) determines if there _{is an unprocessed previous month interest rate X p in the table of monthly interest rate / approximate average interest rate / total cumulative probability.} Initially, X _p = X ₀ . Initially, there is an unprocessed X ₀ . If it is determined that there is an unprocessed previous month interest rate X _{p in} the table, in step 834, the processor 102 (element 1031) has the monthly interest rate / approximate average interest rate / total cumulative probability of the previous month t-1 in the table. Refer to the unprocessed record (row) of.

In step 836, the processor 102 (element 1031) reads each current month interest rate X _{q of the transition destination with respect to the unprocessed previous month interest rate X p} with reference to the interest rate transition probability matrix or table (eg, FIG. 9B), and reads the previous _{month interest rate X q.} Generate a working record of interest rate / approximate average interest rate / current month interest rate (eg, 923 in Figure 12B).

In step 838, processor 102 (element 1031) calculates and approximates the current month's cumulative average interest rate Y _q and the cumulative transition probability C _t (X _q , Y _{q ) for the current month's interest rate X q in each generated work record.} Determine the cumulative average interest rate Z _z. The cumulative transition probability C _t (X _q , Y _q ) for the current month interest rate X _q is the cumulative transition probability C _t-1 of the previous month t-1 and the transition probability S (X _p) from the previous month interest rate X _p to the current month interest rate X _q. , X _q ) and C _t-1 × S (X _p , X _q ). Month cumulative average rate Y _q relates month rate X _q, the sum of the product and month interest X _q previous month t-1 cumulative average rate Z _z from the previous month t-1 to the number of months (t), current month month It is a value divided by a few tons. The processor 102 (element 1031) then receives an approximate cumulative average interest rate Z _z ∈ {x ₁ , x ₂ ,. .. .. , X _N }, the approximate cumulative average interest rate Z _z closest to the cumulative average interest rate Y _q of the current month t is determined as the approximate value of the cumulative average interest rate Y _{q of the current month.} The number of approximate cumulative average rate Z _z to be determined may be one or two. When the number of approximate cumulative average interest rates Z _z is 2, the cumulative transition probability C _t (X _q , Y _q ) is distributed to two approximate cumulative average interest rates Z _z according to the difference from the cumulative average interest rate Y _q. You may.

In step 840, the processor 102 (element 1031) makes a cumulative transition to the total cumulative transition probability C _{q, z} of the current month interest rate X _{q with respect to the obtained approximate cumulative average interest rate Z z} in the table of monthly interest rate / approximate average interest rate / cumulative probability. Add the probability C _t. In this way, a table of monthly interest rate / approximate average interest rate / cumulative probability is generated (eg, FIG. 12B, 924). The procedure then returns to step 832. If it is determined in step 832 that there is no unprocessed previous month interest rate X _p in the table, the procedure returns to step 826 in FIG. 10A.

If it is determined in step 828 of FIG. 8A that the current month t is not less than or equal to the period months M, that is, the current month t exceeds the number of months M, in step 860 the processor 102 (element 1031) relates to each approximate cumulative average interest rate Z _z. The sum of the total cumulative transition probabilities C _{q and z} and the predicted probability of occurrence thereof are calculated and displayed (eg, FIG. 12D).

12A-12C show the approximate cumulative average interest rate and the cumulative transition probability using the monthly interest rate / approximate average interest rate / cumulative probability table and the previous month interest rate / approximate average interest rate / current month interest rate work record according to the flowcharts of FIGS. 10A and 10B. An example of the procedure for finding is shown.

In FIG. 12A, in the initial table 921 of the monthly interest rate / approximate average interest rate / cumulative probability, the current month interest rate X _q = X ₀ = 1.1% and the approximate cumulative average interest rate Z _z = Z _{0 at the initial month t = 0.} = 1.1% and the total cumulative transition probability C _{q, z} = C ₀ (X ₀ , Z ₀ ) = 1.0 are initially set.

Referring to FIG. 12B, assuming that the current month t = 1, in the work record 923 of the previous month interest rate / approximate average interest rate / current month interest rate, the transition destination is set _{to the previous month interest rate X p = 1.1% according to the interest rate transition probability table of FIG. 9B.} There are two current month interest rates of 1.1% and 1.2%, so two records (two lines) are generated. In the first record, in the item of the previous month t-1, from the initial table 921 of FIG. 12A, the previous month interest rate X _p = 1.1%, the approximate cumulative average interest rate Z _z = 1.1%, and the cumulative transition probability C _{t-. 1 = 1 is copied and stored, and the current month interest rate X q} = 1.1% and the transition probability S (X _p , X _q ) = 0.33 are stored in the item of the current month t from the table of interest rate transition probabilities in FIG. 9B. It is copied and stored. In the second record, in the item of t-1 of the previous month, from the initial table 921, the interest rate of the previous month X _p = 1.1%, the approximate cumulative average interest rate Z _z = 1.1%, and the cumulative transition probability C _t-1 = 0. _{.33 is copied and stored, and the current month interest rate X q} = 1.2% and the transition probability 0.67 are copied and stored in the item of the current month t from the table of the cumulative transition probability of FIG. 9B.

Then, in the first record, the cumulative probability C _t of the current month t becomes the cumulative transition probability C _t-1 = (X _p , Z _z ) = 1 of the previous month t-1 and the transition probability S (X _p , X _q ). = 0.33 is multiplied to obtain C _t = 0.33. Next, as described with respect to the state 904 of FIG. 11, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.100% by the monthly weighted average of the cumulative average interest rate Z _z and the interest rate for the current month. Next, the approximate average interest rate Z _z = 1.1%, which is the closest to the cumulative interest rate Y _{q = 1.100% for the current month, is determined.} Then, in the second record, the cumulative transition probability C _t of the current month t becomes the cumulative probability C _t-1 = (X _p , Z _z ) = 1 of the previous month t-1 and the transition probability S (X _p , X _q ). = 0.67 is multiplied to obtain C _t = 0.67. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.150% by the monthly weighted average of the cumulative average interest rate Z _z and the interest rate for the current month, as described above. Next, the approximate average interest rate Z _z = 1.2, which is the closest to the cumulative interest rate Y _{q = 1.150% for the current month, is determined.} In this case, rounding is applied.

Next, in Table 924 of monthly interest rate / approximate average interest rate / cumulative probability, two records _{regarding the approximate average interest rate Z z} = 1.1 and 1.2 in the first and second records of the work record 923 are generated. .. In Table 924, the current month interest rate Z _q = 1.1 and the approximate average interest rate Z _z = 1.1 are copied and stored in _{the first record from the work record 923, and the total cumulative probability C q, z} (initial value 0) is stored. ) Is added with the cumulative probability Ct = 0.33. Further, in Table 924, the current month interest rate Z _q = 1.2 and the approximate average interest rate Z _z = 1.2 are copied and stored in _{the second record from the work record 923, and the total cumulative probability C q, z} (initial). Cumulative probability C _t = 0.67 is added to the value 0). In this way, the monthly interest rate / approximate average interest rate / cumulative probability table 924 for the month t = 1 is generated.

Referring to FIG. 12C, the work record 926 of the current month t = 2 is set as in FIG. 12B. In the work record 926 of FIG. 12C, two records (two rows) are generated for _{the previous month interest rate X p} = 1.1 according to the table of interest rate transition probabilities of FIG. 9B, as in the case of FIG. 12B. In the first record, in the item of t-1 of the previous month, from Table 924 of FIG. 12B, the interest rate of the previous month X _p = 1.1, the approximate average interest rate Z _z = 1.1, and the cumulative probability C _t-1 = 0.33. _{It is copied and stored, and the current month interest rate X q} = 1.1 and the transition probability S (X _p , X _q ) = 0.33 are copied and stored in the item of the current month t from the table of interest rate transition probabilities in FIG. 9B. To. _{In the second record, the previous month interest rate X p} = 1.1, the approximate average interest rate Z _z = 1.1, and the cumulative probability C _t-1 = 1 are copied from Table 804 in FIG. 12B to the item of the previous month t-1. _{The current month interest rate X q} = 1.2 and the transition probability 0.67 are copied and stored in the item of the current month t from the table of interest rate transition probabilities in FIG. 9B.

Next, in the first record, the cumulative probability C _{t of the current month t is obtained as C t} = 0.33 × 0.33 = 0.109 as described above. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.100 as described above. Next, the approximate average interest rate Z _z = 1.1, which is the closest to the cumulative interest rate Y _{q = 1.100 for the current month, is determined.} Next, in the second record, the cumulative probability C _{t of the current month t is calculated as C t} = 0.33 × 0.67 = 0.221 as described above. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.133 as described above. Next, the approximate average interest rate Z _z = 1.1, which is the closest to the cumulative interest rate Y _{q = 1.133% for the current month, is determined.}

Further, in the work record 926, three more records (three rows) are _{similarly generated for the previous month interest rate X p} = 1.2 according to the table of interest rate transition probabilities in FIG. 9B. In the third record, in the item of t-1 of the previous month, from Table 924 of FIG. 12B, the interest rate of the previous month X _p = 1.2, the approximate average interest rate Z _z = 1.2, and the cumulative probability C _t-1 = 0.67. _{It is copied and stored, and the current month interest rate X q} = 1.1 and the transition probability S (X _p , X _q ) = 0.33 are copied and stored in the item of the current month t from the table of interest rate transition probabilities in FIG. 9B. To. In the fourth record, in the item of t-1 of the previous month, from Table 924 of FIG. 12B, the interest rate of the previous month X _p = 1.2, the approximate average interest rate Z _z = 1.2, and the cumulative probability C _t-1 = 0.67. _{It is copied and stored, and the current month interest rate X q} = 1.2 and the transition probability 0.34 are copied and stored in the item of the current month t from the table of interest rate transition probabilities in FIG. 9B. In the fifth record, in the item of t-1 of the previous month, from Table 924 of FIG. 12B, the interest rate of the previous month X _p = 1.2, the approximate average interest rate Z _z = 1.2, and the cumulative probability C _t-1 = 0.67. _{It is copied and stored, and the current month interest rate X q} = 1.3 and the transition probability S (X _p , X _q ) = 0.33 are copied and stored in the item of the current month t from the table of interest rate transition probabilities in FIG. 9B. To.

Next, in the third record, the cumulative probability C _{t of the current month t is calculated as C t} = 0.221 as described above. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.166 as described above. Next, the approximate average interest rate Z _z = 1.2, which is the closest to the cumulative interest rate Y _{q = 1.166 for the current month, is determined.} Next, in the fourth record, the cumulative probability C _{t of the current month t is calculated as C t} = 0.228 as described above. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.200 as described above. Next, the approximate average interest rate Z _z = 1.2, which is the closest to the cumulative interest rate Y _{q = 1.200 for the current month, is determined.} Next, in the fifth record, the cumulative probability C _{t of the current month t is calculated as C t} = 2 as described above. Next, the cumulative interest rate Y _{q for the current month is calculated as Y q} = 1.233 as described above. Next, the approximate average interest rate Z _z = 1.2, which is the closest to the cumulative interest rate Y _{q = 1.233 for the current month, is determined.}

Next, in Table 927 of monthly interest rate / approximate average interest rate / cumulative probability, there are five records relating to the _{approximate average interest rate Z z = 1.1 and 1.2 in the first to fifth fifth records of the work record 926.} Generated. In Table 927, the current month interest rate Z _q = 1.1 and the approximate average interest rate Z _z = 1.1 are copied and stored in _{the first record from the work record 923, and the total cumulative probability C q, z} (initial value 0) is stored. ) Is added with the cumulative probability C _t = 0.109. In Table 927, the current month interest rate Z _q = 1.2 and the approximate average interest rate Z _z = 1.1 are copied and stored in _{the second record from the work record 923, and the total cumulative probability C q, z} (initial value 0) is stored. ) Is added with the cumulative probability C _t = 0.221. In Table 927, the current month interest rate Z _q = 1.1 and the approximate average interest rate Z _z = 1.2 are copied and stored in _{the third record from the work record 923, and the total cumulative probability C q, z} (initial value 0) is stored. ) Is added with the cumulative probability C _t = 0.221. Further, in Table 924, the current month interest rate X _q = 1.2 and the approximate average interest rate Z _z = 1.2 are copied and stored in _{the fourth record from the work record 926, and the total cumulative probability C q, z} (initial). Cumulative probability C _t = 0.228 is added to the value 0). Further, in Table 927, the current month interest rate Z _q = 1.3 and the approximate average interest rate Z _z = 1.2 are copied and stored in _{the fifth record from the work record 926, and the total cumulative probability C q, z} (initial). Cumulative probability C _t = 0.221 is added to the value 0). In this way, the monthly interest rate / approximate average interest rate / cumulative probability table 927 for the month t = 2 is generated.

In this way, the same process is repeated from t = 0 of the current month to t = M of the last month. In this way, the cumulative transition probability of the interest rate transition from the initial interest rate to each approximate average interest rate can be obtained.

Figure 12D shows an example of a generation ratio of each approximate cumulative average rate Z _z to be displayed on the display unit 124 of the information processing apparatus 10. The processor 102 (element 1031) sums the total cumulative transition probabilities C _{q, z for each approximate cumulative average interest rate Z z} for the last month M, and sums all the current month interest rates X _q for each approximate cumulative average interest rate Z _z. Cumulative transition probability C _z of. Next, the processor 102 (element 1031) normalizes the cumulative transition probability C _{z of each approximate cumulative average interest rate Z z} so that the total sum is 1, and predicts the probability of occurrence of _{each approximate cumulative average interest rate Z z.} Or find the ratio. The processor 102 (element 1031) has an initial interest rate of X ₀ = 1.1%, a period of months M = 6 months, and an average interest rate of 1.1% and 1.2% as predicted probabilities or ratios on the display device 124. , 0.34 and 0.66, respectively. In this case, the probability of occurrence of the average interest rates of 1.0% and 1.3% is 0 (zero).

Based on the information displayed in FIG. 12D, the user can determine the interest rate of the corporate bond based on the predicted probability of occurrence of the average interest rate of 1.1% and 1.2% or the ratios of 0.34 and 0.66.

As mentioned above, when predicting the interest rate transition probability based on past experience data, use the number of significant digits after the decimal point when distributing the current month's cumulative average interest rate to the approximate cumulative average interest rate and when calculating the cumulative transition probability. Approximation occurs when approximating and when distributing the cumulative transition probabilities to the sum cumulative probabilities. The calculation error will be larger than when using the number of passes.

According to the embodiment, it is possible to derive the transition of the borrowing interest rate of a short-term bank from the past interest rate data using the high-efficiency algorithm, the average interest rate of a large number of interest rate transition paths, and the frequency or probability of occurrence thereof. It provides an advantageous indicator for determining how much variation the expected profit and loss is expected.

The method using the frequency of occurrence of the interest rate transition path in the embodiment is a simulation based on past experience. Further, the method of the embodiment of the present invention is stochastically valid, and the method based on the transition probability based on experience can obtain a prediction with higher accuracy than any other probability transition matrix.

Next, the validity of the method for predicting the average interest rate based on the experience of the embodiment by the inventor will be described.

According to the inventor's analysis, future interest rate changes are likely to behave similarly to past proven interest rate changes. The transition probabilities S _{p and q} are assumed. Here, p is the interest rate for one month and q is the interest rate for the next month. It is assumed that the transition frequency from the past interest rate p to the interest rate q is m _{p, q} , and the total transition frequency from p to any interest rate is M _p. Then, the transition probability is _{Sp, q} = m _{p, q} / M _p . As a property of interest rate transition probabilities, all past interest rate transition paths have, for example, interest rate transition probabilities S _1,1 , S _1,2 , S _2,1 , S _1,3 ,. .. .. , S _4,5 .

According to the inventor, it is assumed that there are only two interest rates p and q with _{a transition probability S p, q , that is, only S 1} , ₁ , S ₁ , _{2, S 2, 1, S 2, 2.} do. It can be mathematically proved that when the two interest rate transition probabilities C ₁ and C ₂ are set to be proportional to the past occurrence frequency, the probability that best represents the past transition path can be obtained. Next, it can be proved by mathematical induction that if the interest rate of the interest rate transition destination by experience is N, it is also true if the interest rate transition destination is N + 1. Here, the mathematical proof is omitted.

According to the embodiment, the average interest rate calculated at each stage from the start to each period is replaced with or corresponding to the approximate average interest rate of the number actually experienced, so that each average interest rate over a plurality of periods is used. The cumulative number of transition paths can be calculated in a short time by a personal computer. It also requires less storage space to temporarily store the approximate average interest rate and the number of cumulative transition paths than if no such replacement or correspondence was made. For example, the amount of calculation when the approximate average interest rate is applied for a period of 120 months has an advantage that the processing amount is ^{generally 1/10 49 as compared with the case where the approximate average interest rate is not applied.}

The embodiments described above are merely given as typical examples, and combinations, variations and variations of the components of each embodiment are obvious to those skilled in the art, and those skilled in the art are within the scope of the principles and claims of the present invention. It is clear that various modifications of the above embodiments can be made without departing from the scope of the described invention.

Claims (11)

A program for predicting the average of variable interest rates
Based on multiple interest rates in at least a series of past periods, an interest rate transition frequency representing the frequency of interest rate transitions in adjacent periods is generated and stored in the storage.
Read the number of periods of multiple periods and the initial interest rate selected from the multiple interest rates as the interest rate of the initial period and the approximate cumulative average interest rate.
For the multiple periods
Refer to the first interest rate in the period before the period of interest, the first approximate cumulative average interest rate for the first interest rate, and the first cumulative transition path number for the first interest rate in the storage unit.
With reference to the interest rate transition frequency, the second interest rate to which the transition from the first interest rate is made and the transition frequency thereof are determined.
From the first approximate cumulative average interest rate for the first interest rate in the previous period and the second interest rate for the period of interest, the cumulative average interest rate for the second interest rate for the period of interest is obtained.
The second approximate cumulative average interest rate of one or two of the plurality of interest rates closest to the obtained cumulative average interest rate is determined.
Here, the first and second interest rates and the first and second approximate cumulative average interest rates are any of the plurality of interest rates.
Further, the number of the first cumulative transition paths related to the first interest rate in the previous period is multiplied by the transition frequency to obtain the number of the second cumulative transition paths, and at least one of the second cumulative transition paths. The unit is added to the corresponding third cumulative transition path number for the second interest rate and the second approximate cumulative average interest rate in the period of interest and stored in the storage unit.
The second interest rate, the second approximate cumulative average interest rate, and the number of the third cumulative transition paths are the next first interest rate and the next first interest rate in the period before the next period of interest, respectively. A program for causing an information processing apparatus to execute a process including repeating a process used as the next first approximate cumulative average interest rate and the next first cumulative transition path number for the next first interest rate. Further, claim 1, wherein the information processing apparatus is made to execute a process of displaying the total number of the third cumulative transition paths for each of the second approximate cumulative average interest rates in the last period of the plurality of periods. Program. The cumulative average interest rate obtained up to the period of interest for each combination of the first approximate cumulative interest rate and the second interest rate in the previous period is the first approximate cumulative average interest rate and the previous period. The program according to claim 1 or 2, wherein the product of the number of periods up to and the sum of the second interest rate is divided by the number of periods up to the period of interest. When the second approximate cumulative average interest rate closest to the calculated cumulative average interest rate is the third approximate cumulative average interest rate and the fourth approximate cumulative average interest rate, the second cumulative transition to the calculated cumulative average interest rate. A part of the number of passes is added to the number of the third cumulative transition paths related to the second interest rate and the third approximate cumulative average interest rate, and the rest of the second cumulative transition paths is the second. The program according to any one of claims 1 to 3, wherein the program is added to the number of the third cumulative transition paths relating to the interest rate and the fourth approximate cumulative average interest rate. The part of the number of the second cumulative transition paths added to the number of the third cumulative transition paths relating to the second interest rate and the third approximate cumulative average interest rate is the obtained cumulative average interest rate and the first. The program according to claim 4, characterized in that the difference between the approximate cumulative average interest rates of 3 tends to increase as the difference decreases. A method for predicting the average of variable interest rates,
Based on multiple interest rates in at least a series of past periods, an interest rate transition frequency representing the frequency of interest rate transitions in adjacent periods is generated and stored in the storage.
Read the number of periods of multiple periods and the initial interest rate selected from the multiple interest rates as the interest rate of the initial period and the approximate cumulative average interest rate.
For the multiple periods
Refer to the first interest rate in the period before the period of interest, the first approximate cumulative average interest rate for the first interest rate, and the first cumulative transition path number for the first interest rate in the storage unit.
With reference to the interest rate transition frequency, the second interest rate to which the transition from the first interest rate is made and the transition frequency thereof are determined.
From the first approximate cumulative average interest rate for the first interest rate in the previous period and the second interest rate for the period of interest, the cumulative average interest rate for the second interest rate for the period of interest is obtained.
The second approximate cumulative average interest rate of one or two of the plurality of interest rates closest to the obtained cumulative average interest rate is determined.
Here, the first and second interest rates and the first and second approximate cumulative average interest rates are any of the plurality of interest rates.
Further, the number of the first cumulative transition paths related to the first interest rate in the previous period is multiplied by the transition frequency to obtain the number of the second cumulative transition paths, and at least one of the second cumulative transition paths. The unit is added to the corresponding third cumulative transition path number for the second interest rate and the second approximate cumulative average interest rate in the period of interest and stored in the storage unit.
The second interest rate, the second approximate cumulative average interest rate, and the number of the third cumulative transition paths are the next first interest rate and the next first interest rate in the period before the next period of interest, respectively. A method in which an information processing apparatus executes a process including repeating a process used as the next first approximate cumulative average interest rate and the next first cumulative transition path number for the next first interest rate. An information processing device for predicting the average of variable interest rates.
A first processing unit that generates and stores an interest rate transition frequency representing the frequency of interest rate transitions in adjacent periods based on a plurality of interest rates in at least a series of past periods, and a storage unit.
A second processing unit that reads the number of periods of a plurality of periods and the initial interest rate selected from the plurality of interest rates as the interest rate of the initial period and the approximate cumulative average interest rate.
For the multiple periods
Refer to the first interest rate in the period before the period of interest, the first approximate cumulative average interest rate for the first interest rate, and the first cumulative transition path number for the first interest rate in the storage unit.
With reference to the interest rate transition frequency, the second interest rate to which the transition from the first interest rate is made and the transition frequency thereof are determined.
From the first approximate cumulative average interest rate for the first interest rate in the previous period and the second interest rate for the period of interest, the cumulative average interest rate for the second interest rate for the period of interest is obtained.
The second approximate cumulative average interest rate of one or two of the plurality of interest rates closest to the obtained cumulative average interest rate is determined.
Here, the first and second interest rates and the first and second approximate cumulative average interest rates are any of the plurality of interest rates.
Further, the number of the first cumulative transition paths related to the first interest rate in the previous period is multiplied by the transition frequency to obtain the number of the second cumulative transition paths, and at least one of the second cumulative transition paths. The unit is added to the corresponding third cumulative transition path number for the second interest rate and the second approximate cumulative average interest rate in the period of interest and stored in the storage unit.
The second interest rate, the second approximate cumulative average interest rate, and the number of the third cumulative transition paths are the next first interest rate and the next first interest rate in the period before the next period of interest, respectively. A second processing unit that repeats the processing used as the next first approximate cumulative average interest rate and the next first cumulative transition path number for the next first interest rate.
Information processing equipment including. A program for predicting the average of variable interest rates
Based on a plurality of interest rates in at least a series of past periods, interest rate transition frequency data representing the frequency of interest rate transitions in adjacent periods is generated, and from the plurality of interest rates to the plurality of interest rates based on the interest rate transition frequency data. Generate the interest rate transition probability of and store it in the storage
Read the number of multiple periods and the initial interest rate selected from the multiple interest rates as the interest rate for the initial period and the approximate cumulative average interest rate.
For the multiple periods
Refer to the first interest rate in the period before the period of interest, the first approximate cumulative average interest rate for the first interest rate, and the first cumulative transition probability for the first interest rate in the storage unit.
With reference to the interest rate transition probability, the second interest rate of the transition destination from the first interest rate and the transition probability thereof are determined.
From the first approximate cumulative average interest rate for the first interest rate in the previous period and the second interest rate for the period of interest, the cumulative average interest rate for the second interest rate for the period of interest is obtained.
The second approximate cumulative average interest rate of one or two of the plurality of interest rates closest to the obtained cumulative average interest rate is determined.
Here, the first and second interest rates and the first and second approximate cumulative average interest rates are any of the plurality of interest rates.
Further, the first cumulative transition probability for the first interest rate in the previous period is multiplied by the transition probability to obtain the second cumulative transition probability, and at least a part of the second cumulative transition probability is obtained. It is added to the corresponding third cumulative transition probability of the second interest rate and the second approximate cumulative average interest rate of the period of interest and stored in the storage unit.
The second interest rate, the second approximate cumulative average interest rate, and the third cumulative transition probability are related to the next first interest rate and the next first interest rate in the period before the next period of interest, respectively. A program for causing an information processing apparatus to execute a process including repeating a process used as the next first approximate cumulative average interest rate and the next first cumulative transition probability with respect to the next first interest rate. Further, claim 8, wherein the information processing apparatus is made to execute a process of displaying the sum of the third cumulative transition probabilities for each of the second approximate cumulative average interest rates in the last period of the plurality of periods. program. A method for predicting the average of variable interest rates,
Based on a plurality of interest rates in at least a series of past periods, interest rate transition frequency data representing the frequency of interest rate transitions in adjacent periods is generated, and from the plurality of interest rates to the plurality of interest rates based on the interest rate transition frequency data. Generate the interest rate transition probability of and store it in the storage
Read the number of multiple periods and the initial interest rate selected from the multiple interest rates as the interest rate for the initial period and the approximate cumulative average interest rate.
For the multiple periods
Refer to the first interest rate in the period before the period of interest, the first approximate cumulative average interest rate for the first interest rate, and the first cumulative transition probability for the first interest rate in the storage unit.
With reference to the interest rate transition probability, the second interest rate of the transition destination from the first interest rate and the transition probability thereof are determined.
From the first approximate cumulative average interest rate for the first interest rate in the previous period and the second interest rate for the period of interest, the cumulative average interest rate for the second interest rate for the period of interest is obtained.
The second approximate cumulative average interest rate of one or two of the plurality of interest rates closest to the obtained cumulative average interest rate is determined.
Here, the first and second interest rates and the first and second approximate cumulative average interest rates are any of the plurality of interest rates.
Further, the first cumulative transition probability for the first interest rate in the previous period is multiplied by the transition probability to obtain the second cumulative transition probability, and at least a part of the second cumulative transition probability is obtained. It is added to the corresponding third cumulative transition probability of the second interest rate and the second approximate cumulative average interest rate of the period of interest and stored in the storage unit.
The second interest rate, the second approximate cumulative average interest rate, and the third cumulative transition probability are related to the next first interest rate and the next first interest rate in the period before the next period of interest, respectively. A method in which an information processing apparatus executes a process including repeating a process used as the next first approximate cumulative average interest rate and the next first cumulative transition probability with respect to the next first interest rate. Based on a plurality of interest rates in at least a series of past periods, interest rate transition frequency data representing the frequency of interest rate transitions in adjacent periods is generated, and from the plurality of interest rates to the plurality of interest rates based on the interest rate transition frequency data. The first processing unit that generates the interest rate transition probability of and stores it in the storage unit,
A second processing unit that reads a plurality of periods and an initial interest rate selected from the plurality of interest rates as the interest rate of the initial period and the approximate cumulative average interest rate.
For the multiple periods
Refer to the first interest rate in the period before the period of interest, the first approximate cumulative average interest rate for the first interest rate, and the first cumulative transition probability for the first interest rate in the storage unit.
With reference to the interest rate transition probability, the second interest rate of the transition destination from the first interest rate and the transition probability thereof are determined.
From the first approximate cumulative average interest rate for the first interest rate in the previous period and the second interest rate for the period of interest, the cumulative average interest rate for the second interest rate for the period of interest is obtained.
The second approximate cumulative average interest rate of one or two of the plurality of interest rates closest to the obtained cumulative average interest rate is determined.
Here, the first and second interest rates and the first and second approximate cumulative average interest rates are any of the plurality of interest rates.
Further, the first cumulative transition probability for the first interest rate in the previous period is multiplied by the transition probability to obtain the second cumulative transition probability, and at least a part of the second cumulative transition probability is obtained. It is added to the corresponding third cumulative transition probability of the second interest rate and the second approximate cumulative average interest rate of the period of interest and stored in the storage unit.
The second interest rate, the second approximate cumulative average interest rate, and the third cumulative transition probability are related to the next first interest rate and the next first interest rate in the period before the next period of interest, respectively. A second processing unit that repeats the processing used as the next first approximate cumulative average interest rate and the next first cumulative transition probability for the next first interest rate.
Information processing equipment including.

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