JP2007172348A - Apparatus for estimating residual value and premium calculation apparatus with means for estimating residual value - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To estimate residual value with higher accuracy and calculate an appropriate premium based on it. <P>SOLUTION: In order to estimate the residual value ratio of a used product with higher accuracy, an apparatus calculates an estimated residual value ratio that reflects the basic value of the used product, based on the Weibull distribution. Further, based on an OU process the apparatus calculates an estimated value of the dispersion of the logarithm of the residual value ratio reflecting the market value of the used product, and uses predetermined parameter values to calculate premium that reflect these expectations. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a premium calculation apparatus including a residual value prediction apparatus and a residual value prediction means.

  Conventionally, instead of individuals or corporations purchasing products, leasing companies purchase products, lending products to individuals or corporations for a certain period of time, and consumers paying lease fees to leasing companies. Lease products are in circulation. For example, in automobile leasing, a product is known in which a value (residual value) in the used market of the car at the time of lease expiration is set in advance, and the lease fee is determined by subtracting the residual value from the vehicle price. There are open end leases and closed end leases that take account of such residual value. An open-end lease is a method that settles the difference between the residual value initially set at the contract and the actual price of the target item at the second-hand market at the time of expiration. Closed-end lease is a method of returning an object to a leasing company without adjusting the residual value of the object, and the residual value set at the time of contract is guaranteed as it is. Therefore, closed-end leases are less risky for users of leased products. In addition, the higher the residual value at the time of contract, the more attractive the lease product for the user. However, for the leasing company, if the actual residual value of the leased item exceeds the set residual value at the time of contract, it will be a profit for the leasing company. If it is lower than the set residual value, the loss will be incurred. This residual value is usually set empirically by a leasing company.

  In residual value guarantee-type leases including loans, the risk that the residual value preset at the time of the lease contract falls below the residual value at the end of the lease (the actual price of the object in the secondhand market) is called residual value risk. In the case of closed-end leases, the leasing company bears this residual value risk. Therefore, insurance that guarantees this residual value risk, for example, used car residual value guarantee insurance is conceivable. In other words, if the residual value (rate) preset at the time of the lease contract falls below the residual value (rate) at the end of the lease (the price of the used car in the actual used market), the insurance pays insurance according to the degree It is. Therefore, it is important for insurance companies to predict the value (residual value) of a used car at the end of the contract, but in general, this residual value is empirically predicted from past trends, etc. You have to set a premium.

Thus, there is a disclosure of Patent Document 1 as a system for calculating insurance premiums for residual value guarantee insurance. In Patent Document 1, a residual value is predicted, and an insurance premium is calculated based on the predicted residual value. However, forecasting the residual value of the target products in the future is a very important factor in the above-mentioned residual value guarantee type lease products and residual value guarantee insurance, and more accurate residual value forecasts are required. .
JP 2003-216819 A

  In view of the above, for residual value guaranteed lease products and residual value guaranteed insurance, it is possible to perform more accurate residual value forecasts, and to calculate appropriate insurance premiums based on more accurate residual value predictions A possible device is required.

  The residual value rate prediction apparatus according to the present invention is a used price data storage means for storing used price data including residual value rate data, which is a ratio of used product price to new product price, and elapsed time data of the used product. A first parameter value calculating means for applying a Weibull distribution model formula to the used price data, calculating a value of a first parameter group that defines the Weibull distribution of the residual value rate, and outputting the value First parameter value storage means for storing the output value of the first parameter group, and the used price data, an Orstein-Uhlenbeck process (hereinafter referred to as OU process) model. A second parameter value calculation that calculates the value of the second parameter group that defines the OU process related to the residual value rate and outputs the value by applying the equation And the second parameter value storage means for storing the value of the output second parameter group, and the calculated and stored value of the first parameter group, based on the Weibull distribution, Using the predicted residual value rate calculating means for calculating the predicted residual value rate of the second-hand goods and outputting the predicted residual value rate, and the value of the second parameter group calculated and stored, the OU process is performed. Based on this, it is possible to provide a distributed predicted value calculation means for calculating a predicted value of variance of the logarithmic value of the residual value rate and outputting the predicted value. Here, using the value of the first parameter group includes using at least one value of the first parameter group, and using the value of the second parameter group is the second Using at least one of the values of the parameter group.

The residual value rate prediction apparatus according to the present invention can be configured such that the first parameter value calculation unit and the predicted residual value rate calculation unit perform calculation using a Weibull distribution model formula. Here, the Weibull distribution model formula can be defined as follows.

In the above equation, S (t) is the residual value rate of the target product at time t, p is an initial residual value parameter whose value is given in advance, α is a parameter called a shape parameter, β is a parameter called scale parameter, and γ is a parameter called rotation. K represents the time when the target product is introduced into the market. In the above equation, α and β can be set as the first parameter group.

  In the residual value rate prediction apparatus according to the present invention, the first parameter value calculation unit and the predicted residual value rate calculation unit are configured to perform calculation using another model formula based on the Weibull distribution. May be.

The residual value rate prediction apparatus according to the present invention can be configured such that the second parameter value calculation means and the distributed prediction value calculation means perform calculations using an OU process model equation. Here, the OU process model equation can be defined as follows.

Note that r indicates a residual value rate, and var [logr] indicates a logarithmic variance of the residual value rate r. Moreover, e ^s is the initial volatility parameters previously its value is given. t indicates a point in time after the lapse period of the target product (for example, in the case of a car lease, when the contracted lease period ends), and k indicates a point in time when the target product is put on the market. Θ is a parameter indicated as an average regression coefficient, and σ is a parameter indicating volatility (variance). In the OU process model equation, θ and σ can be set as the second parameter group.

  In the residual value rate prediction apparatus according to the present invention, the second parameter value calculation means and the distributed prediction value calculation means are configured to perform calculations using other model expressions based on the OU process. Also good.

  In addition, the insurance premium calculation device according to the present invention is a used price data storage for storing used price data including residual value rate data, which is a ratio of a used product price to a new product price, and elapsed time data of the used product. Means for applying a Weibull distribution model formula to the used price data, calculating a value of a first parameter group defining the Weibull distribution of the residual value rate, and outputting the value Means, a first parameter value storage means for storing the output value of the first parameter group, and an OU process model formula is applied to the used price data to define an OU process relating to the residual value rate. A second parameter value calculating means for calculating a value of the second parameter group and outputting the value; a second parameter value storing means for storing the output value of the second parameter group; There can be provided insurance premium calculation means for calculating an insurance premium using the stored value of the first parameter group and the stored value of the second parameter group and outputting the insurance premium. . Here, the use of the stored value of the first parameter group and the stored value of the second parameter group means that at least one of the values of the first parameter group and the second parameter are used. Using at least one of the values of the group.

  Here, the Weibull distribution model formula indicates the formula defined above. In the insurance premium calculation apparatus according to the present invention, the first parameter value calculation means may be configured to perform calculation using another model formula based on the Weibull distribution.

  The OU process model formula indicates the formula defined above. In the insurance premium calculation apparatus according to the present invention, the second parameter value calculation means may be configured to perform calculation using another model formula based on the OU process.

Moreover, the insurance premium calculation apparatus according to the present invention can be configured such that the insurance premium calculation means calculates using an insurance premium calculation formula. Here, the insurance premium calculation formula is defined as follows.

In the above formula, the upper and lower limit l of the insurance premium is obtained for the number of used vehicles U to Poisson (λ) and the independent identical distribution (iid) normal random variables Z _{n to} N (0, 1). Here, K is a contract residual value (residual value set at the time of contract), t is a time point, and k is a model type of a vehicle model. In addition, p is an initial residual value rate parameter, and r indicates a planned interest rate. The parameters α, β, θ, and σ can be substituted with the values of the parameter groups calculated by the first parameter calculation means and the second parameter calculation means, respectively. Here, the upper and lower limit l of the insurance premium can be used as the insurance premium.

  In the insurance fee calculation apparatus according to the present invention, the insurance fee calculation means is calculated by the first parameter calculation means and stored in the first parameter group value and the second parameter calculation means. You may comprise so that an insurance premium may be calculated from another model type | formula using the value of the 2nd parameter group calculated and memorize | stored.

  The apparatus according to the present invention is an apparatus realized using a computer having at least an input unit, a calculation unit, and a storage unit.

  Of the terms used in this specification and claims, input means means input means by user operation such as a keyboard and a mouse, input by a recording medium such as a floppy (registered trademark) disk, a communication line, Means for receiving an input by an electrical signal such as a LAN (Local Area Network). The storage means is means for storing data such as characters and numbers, programs, and the like. For example, a random access memory or a hard disk in a computer. The calculation means is a numerical calculation means for executing a program. For example, it is generally called a central processing unit or CPU. A computer refers to an electronic computer including at least input means, storage means, and calculation means as described above.

  The apparatus according to the present invention may be realized by a single computer or may be realized by a plurality of computers on a network.

  The value (residual value) of the future used goods in the future depends on the life expectancy of the used goods (for example, in the case of used cars, the car must be able to run normally after a certain period of time) (basic value) Apart from basic value and value, it is considered to be determined by the market's fluid value (market value), such as popularity of second-hand goods and supply-demand relationships. In the present invention, the basic value is reflected by using the Weibull distribution model formula based on the Weibull distribution, and the market value is reflected by using the OU process model formula based on the OU process. The residual value rate can be predicted. An appropriate insurance premium can be calculated based on such a highly accurate prediction of the residual value rate.

  Embodiments of the present invention will be described below with reference to the accompanying drawings. FIG. 1 shows a configuration diagram of a residual value rate prediction apparatus according to the first embodiment of the present invention. The residual value rate prediction apparatus 10 can be realized by cooperating a general computer and software. That is, hardware resources such as the input means 12, the computing means 14, and the storage means 16 of the computer can be specifically operated by software to realize the operation as a dedicated device.

  In the residual value rate prediction apparatus 10, the calculation means 14 includes a first parameter value calculation unit 20, a second parameter value calculation unit 22, a prediction residual value rate calculation unit 24, and a distributed prediction value calculation unit 26. . The storage unit 16 includes a first parameter value storage unit 30, a second parameter value storage unit 32, and a used car price data storage unit 36.

  The first parameter value storage unit 30 stores the value of the first parameter group output from the first parameter value calculation unit 20. The second parameter value storage unit 32 stores the value of the second parameter group output from the second parameter value calculation unit 22. The used car price data storage unit 36 stores used car price data relating to the price of used cars. The used car price data storage unit 36 includes a used car price initial data storage unit (not shown) for storing used car price initial data.

  In this embodiment, the used car price initial data includes the year, month and day data of the used car auction date, the year, month and day data of the first year registration date, and the year of the vehicle inspection date for each car. , Month and day data, new car prices, and used car prices actually used in used car auctions.

  In this embodiment, in order to exclude the influence of the remaining period of vehicle inspection from the price of used cars, the vehicle inspection is based on the difference between the date of the used car auction and the date of the inspection. The remaining period (in months) of the car is calculated, and the amount multiplied by a predetermined constant is subtracted from the original used car price data (auction successful bid price data), and the value is used as the used car price data. Yes.

  Based on the used car price initial data, the calculation means 14 calculates the elapsed period of the actual used car (the period from when the new car is delivered until it is sold as a used car) and the actual residual value rate. For example, the elapsed period can be obtained by calculating the period between the first year registration date and the used car auction date. In this embodiment, the elapsed period data is calculated on a monthly basis. The residual value rate is defined as used car price / new car price. Therefore, the actual residual value rate can be obtained from the price data of the new car and the price data of the used car. In the present embodiment, residual value rate data for each elapsed period (monthly) is used. The residual value rate data and the elapsed period data obtained from the used car price initial data are stored in the used car price data storage unit 36 as used car price data.

  Next, the residual value rate prediction processing in the present embodiment will be described using the flowchart shown in FIG. The residual value rate prediction apparatus 10 receives the used car price initial data by the input means 12 (step 10). From the received used car price initial data, an elapsed period and a residual value rate are calculated for each data (step 12). A value of a first parameter group that defines the Weibull distribution is calculated based on the Weibull distribution model formula using the elapsed period and residual value rate data (step 14). A predicted residual value rate is calculated based on the Weibull distribution model equation using the calculated value of the first parameter group, and displayed on a graph (step 16). In addition, the value of the second parameter group that defines the OU process is calculated based on the OU process model equation using the data of the elapsed period and the residual value rate (step 18). Based on the calculated value of the second parameter group, based on the OU process model formula, a predicted value of the variance of the logarithmic value of the residual value rate is calculated and displayed on the graph (step 20).

  In addition to the value (basic value) and basic value that depend on the life expectancy of a vehicle, the value of the vehicle body that can be found in using the vehicle body in the future is a fluidity in the market such as the popularity of the vehicle type and the supply-demand relationship. It is considered that it is determined by a certain value (market value). In the present invention, this basic value can be set as a survival probability using the hazard rate based on the concept of reliability engineering. The survival probability can be expressed by a Weibull distribution that fits empirically with industrial products, human life, and the like. In the present embodiment, a Weibull distribution model formula is set based on the Weibull distribution, and a parameter value that defines the Weibull distribution is calculated and determined based on past data. Then, a predicted residual value rate is calculated using the value of this parameter. In terms of market value, the logarithmic value is Ornstein-Uhlenbeck because it is more natural for the used car market to return to a certain level rather than simply spreading noise over time. According to the process (Orstein-Uhlenbeck process), the parameter value defining the OU process is calculated and determined based on past data. Then, the value of this parameter is used to calculate the residual volatility prediction volatility (variance) (the logarithmic value variance prediction value of the residual value rate).

  Details of steps 14 and 16 are shown in the flowchart of FIG. From the elapsed period (monthly) and the corresponding residual value rate data, the average value of the residual value rate is calculated for each different elapsed period (monthly) (step 141). Next, the value of the first parameter group is calculated from the Weibull distribution model equation using the elapsed period (monthly) and the residual value rate (average value) corresponding to the elapsed period (step 143). Then, using the value of the first parameter group calculated in step 143 and the initial residual value parameter value P given in advance, the predicted residual value rate is calculated from the Weibull distribution model equation and displayed on the graph (step) 160).

  Here, the Weibull distribution model formula will be described. The Weibull distribution model formula is defined based on the Weibull distribution that is easy to fit with industrial products, human life, and the like. In the present embodiment, in calculating the predicted residual value rate, the property that the basic part of the value of a used car depends on the remaining life of the car is taken into consideration. That is, the basic price of a used car is determined by how long it can normally run based on the time when it is bought and sold as a used car. The basic behavior of used car prices can be modeled in the same way as life analysis or reliability analysis that deals with life of organisms and machine / system failures.

The survival probability (corresponding to the residual value rate in the present embodiment) can be expressed by a Weibull distribution that easily fits empirically in terms of industrial products and human life. Here, the survival probability indicates the probability that the vehicle can travel normally after a certain point in time. In addition, in the process of parameter estimation, the inventor does not set the value at the time when the elapsed period is zero as the new car price, but at the moment when the new car is put on the market, the value drops in a stepped manner (so-called new and old). We verified that the model that the basic value decreases according to the Weibull distribution fits well. Therefore, the residual value rate S (t) is defined by the following Weibull distribution model formula.

Here, R (t) is the cumulative scrap car rate, S (t) is the residual value rate, p is the initial residual value rate, and 1-p is the value that is depreciated instantaneously when a new car is introduced to the market. Represents. The “scrap car rate” here refers not to the physical scrap car rate but to the probability of scrap car as the loss rate of economic value. Α is a parameter called a shape parameter, β is a parameter called a scale parameter, and γ is a parameter called rotation. Here, γ is set to zero. In addition, the year type (year of full model change, for example, in the case of a certain car model, October 1994 released and December 1999 of full model change and two year type) In other words, k represents a point in time when a new model car is put on the market. Therefore, tk can be defined as an elapsed period using this year-type data k. However, in this embodiment, in order to calculate the predicted residual value rate without using the year data of the car, k = 0 is set, and t itself is the elapsed period. Therefore, here, the change in economic value reflecting the probability that the vehicle can travel normally after the t elapsed period is shown as the predicted residual value rate. The first parameter group to be calculated is α and β. Since k and γ are zero here, the relationship between the elapsed period t and the residual value rate S is determined by obtaining the values of the three parameters p, α, and β. The value P of the initial residual value parameter p is given to the residual value prediction device 10 in advance. In this embodiment, the initial residual value parameter value P is an arbitrary numerical value between 0 and 1, and is accepted by the input means 12 or the number of the initial residual value parameters p is input, whereby the device 10 Thus, the automatically specified number of initial residual value rate parameter values P are generated.

A method for calculating the values of the parameters α and β will be described below. First, the following equation is obtained by taking the logarithm of the logarithm of both sides of the equation relating to S (t).

here,

By putting

This relationship can be derived. k is zero, and an elapsed period (monthly) t, a residual value rate (average value) S corresponding to the elapsed period, and a value P of a parameter p given in advance are given to the above equation, and x and y are calculate. This calculation is performed for each value of P for each elapsed period (in units of months) and residual value rate (average value) data corresponding to the elapsed period, and a data group of x and y is generated for each value of P.

Since x and y have a linear relationship, the parameters α and β can be calculated from the following equations by the least square method. This calculation is performed for the data group of x and y calculated with each P value, and the values of α and β are uniquely determined for each P value.

For each P value, the fitness (determination coefficient R ² ) of the Weibull distribution model equation using the calculated α and β parameter values is calculated from the following equation.

As described above, the parameter values of α and β and the fitness R ² value of the Weibull distribution model equation when using the parameter values are calculated for each P value. FIG. 5 shows an output result of the calculated data as an example.

Here, the P value and the parameter values of α and β of the group having the maximum fitness R ² value are selected, and the parameter value of the Weibull distribution model formula is determined. The predicted residual value rate S (t) in the elapsed period t is calculated from the Weibull distribution model formula for which the parameter value is determined.

In the present embodiment, the calculated predicted residual value rate and the actual residual value rate (actually measured value) calculated based on used car price data are shown in a graph. An example of this graph is shown in FIG. FIG. 6 shows, as an example, an actual value of used car price average residual value rate in M types of cars and a predicted value based on the Weibull distribution (in the case of P = 0.75 in the output result shown in FIG. 5). From the output result of such data, it can be confirmed how much the calculated predicted residual value rate is different from the actual residual value data. When selecting the maximum value as the fitness R ² value, if there are multiple maximum values or close to the maximum value, there is a slight difference, corresponding to each R ² value The value of each parameter (p, α, β) to be obtained is acquired, the Weibull distribution model formula for each value is determined, and the predicted residual value rate is calculated. Then, as described above, each predicted residual value rate is compared with the actual residual value rate, and the predicted residual value rate that is most dissimilar from the actual residual value data is determined as the predicted residual value rate to be obtained. Is possible.

Next, details of steps 18 and 20 are shown in the flowchart of FIG. From the elapsed period (monthly) and the corresponding residual value rate data, the logarithmic value of the residual value rate and the average value of each elapsed period (monthly) for each auction month are calculated (step 181). Further, a variance of logarithmic values of the residual value rate for each elapsed period (monthly) for each auction opening month is calculated (step 183). Using the calculated variance value, the value of the second parameter group is calculated from the OU process model equation (step 185). Then, using the value E _s initial volatility parameters given in advance and the second value of the parameter group that has been calculated in step 185, it calculates a predicted value of the variance of the logarithm of the residual value ratio from OU process model formula ( Step 200).

  Here, the OU process model formula is used to calculate the insurance premium in consideration of the market value that affects the residual value rate. Market value is expressed by a probabilistic model used in pricing derivatives. However, unlike the stock market, the used car market is not enormous in volume, so it is more natural for noise to return to a certain level rather than simply spreading over time. The inventor verified that the numbers follow the OU process.

The OU process is the one in which the Brownian drift term has an average recursive property. Specifically, the probability of a low value increases when the value is higher than the average, and the probability of the next higher value increases when the value is a low level. It is a kind of average regression process. The OU process X _t is a unique solution that satisfies the following stochastic differential equation.

In the probabilistic model, the logarithmic value of the used car price follows the OU process, but this is to prevent the used car price from becoming a negative value. The logarithm causes an unnecessary trend for price fluctuations, which needs to be corrected. For this reason, the market value fluctuation process Y _t is determined next.

Here, W _t is a standard Wiener process according to a normal distribution with mean 0 and variance t, μ is a parameter representing a long-term average, σ is a parameter representing a short-term standard deviation, and θ is a parameter representing a speed of average regression. It is. Assuming the solution of the above equation is martingale, excluding trend terms that have no economic significance.


Here, T is a parameter indicating a point in time, and k is a parameter indicating a model type of the vehicle model. From the above formula:

It becomes.

Used car price with basic value added to market value

Follows the following stochastic process.

here

Is a random variable introduced to express the seasonal variation element as the fluctuation of the new car price in the new car registration month, and here it is treated as a random variable instead of a constant.

The distribution follows the normal distribution that depends on the elapsed time and the new car registration month, but the average is also affected by the variance. For this reason, parameter estimation becomes a nonlinear regression problem, which is very complicated, and is solved here as a linear regression problem. I want to estimate here

Variance

However, since the variance is an index representing the degree of variation around the average value,

There is no change in the dispersion even if it is translated by the average amount. Therefore, the following formula is established.

Furthermore, if you fix the elapsed time here

The third term of

Unnecessary trends generated by taking the logarithm of と な り are constants and do not affect the calculation of variance. At the same time, the second term, that is, the original trend is also a constant, and p is also a constant, so these also do not affect the dispersion. Therefore, the above equation can be rewritten as follows.

When this is transformed, the following equation is obtained.

here

Is given,


By leaving

Therefore, θ can be estimated by regression analysis. For this purpose, θ is obtained by the least square method using actually measured data. In order to increase the data necessary for fitting, the variance is calculated every auction month (i). From the above, θ is obtained by the following equation.

On the other hand, it does not solved the e ^s as a linear regression problem, determine the coefficient of determination R ² to maximize. Using unbiased estimators,

It can be asked.

Here, a specific flow of data processing using the model will be described. As shown in step 181 and step 183, each elapsed period (monthly) for each auction holding month, the corresponding residual value rate, and the logarithm of the residual value rate are calculated, and the residual value rate is calculated. Find the logarithmic variance. For example, when there are 20 pieces of data corresponding to the auction month of March and the elapsed period of 10 months, logarithmic values of the residual value rates calculated in step 181 are logr _{1 to} logr ₂₀ . And the average of those logarithmic values

Then, the unbiased variance of the logarithmic value of the residual value rate is obtained as follows.

Since the auction month is 12 months, if there are n types of data in different elapsed periods in each month, there will be 12 × n data. For each data, after calculating y, x, c as follows,


Return to the regression equation These equations correspond to the equations 27 and 28 described above. In the present embodiment, as described above, since k in Formula 27 is zero, the formula of x can be expressed as described above. Also, in Equation 27

Corresponds to var [logr], so the expression of y can be expressed as above. In addition, as with the parameter value of the Weibull distribution model formula,

From this, the parameter θ is obtained. Further, the coefficient of determination R ² is similarly obtained from the following. These correspond to Equation 30 above.

In calculating the above parameters, the above formula

The value E _s initial volatility parameters e ^s is given in advance residual value ratio predicting device 10 as the initial value in. In the present embodiment, the parameter E _s is any number between 0 and 1, or is accepted by the input unit 12, by the number of parameter E _s is inputted, the device 10, is automatically designated the value of E _s number was is generated. For each E _s values, values of the R ² of the above parameters θ are calculated. Also, for each E _s values, calculated parameter θ value and the given expression

From this, the value of the parameter σ is calculated.

Using the parameters θ and σ obtained as described above, a predicted value of variance of the logarithmic value of the residual value rate in the elapsed period t can be calculated from the following equation.

FIG. 7 shows an output result of the calculated data as an example.

Here, adaptability of the set of R ² value is maximized, selecting the parameter values of E _s values and theta, determines the parameter values of the OU process model formula. A predicted value var [logr] of the variance of the logarithmic value of the residual value rate in the elapsed period t is calculated from the OU process model formula in which the parameter value is determined.

In the present embodiment, the average value (measured value) of the logarithm of the actual residual value rate obtained for each different elapsed period (monthly) and the calculated residual value rate in the elapsed period t The predicted value of the variance of the logarithmic value is displayed in a graph. An example of this graph is shown in FIG. In FIG. 8, as an example, the average (measured value) of the logarithmic value variance of the residual value rate of the used car price in the M model and the predicted value by the OU process (E _s = 0.4 in the output result shown in FIG. 7). Case). From the output result of such data, it can be confirmed how much the calculated predicted value deviates from the average variance of the logarithmic value of the actual residual value rate. When selecting the maximum value as the fitness R ² value, if there are multiple maximum values or close to the maximum value, there is a slight difference, corresponding to each R ² value Each parameter (E _s , θ) value to be obtained is acquired, an OU process model expression for each value is determined, and each predicted value is calculated. Then, as described above, the predicted value of each variance is compared with the actual variance value data, and the predicted value that is the most different from the actual variance value data can be determined as the predicted value to be obtained. is there. In an example of the data output result shown in FIG. 7, R ² values are monotonically increasing narrowly. Therefore, some candidate values (E _s = 0.4 as an example in the case of the graph shown in FIG. 8) are compared with actual variance value data as shown in FIG. If the lease period is 36 months, it is possible to determine the parameter value when the most disparity from the actual variance value data is around 36 months as the parameter value, and to determine the predicted value to be obtained.

  By providing a projected residual value ratio that reflects the impact of the basic value of the car and a predicted variance of the logarithm of the residual value ratio that reflects the impact of the market value, The leasing company can set a more appropriate residual value rate at the time of lease contract. In insurance such as used car residual value guarantee insurance that guarantees residual value risk, it is possible to set an appropriate insurance premium based on the data predicted by the present invention.

  Next, FIG. 9 shows a configuration diagram of an insurance premium calculation apparatus 100 according to the second embodiment of the present invention. The insurance fee calculation device 100 is realized by causing a general computer and software to cooperate with each other. That is, hardware resources such as the input unit 112, the calculation unit 114, and the storage unit 116 of the computer are specifically operated by software to realize the operation as a dedicated device.

  In the insurance premium calculation apparatus 100, the calculation means 114 includes a first parameter value calculation unit 120, a second parameter value calculation unit 122, a predicted residual value rate calculation unit 124, a distributed predicted value calculation unit 126, and an insurance premium calculation unit 128. And. The storage unit 116 includes a first parameter value storage unit 130, a second parameter value storage unit 132, and a used car price data storage unit 136.

  The first parameter value storage unit 130 stores the value of the first parameter group output from the first parameter value calculation unit 120. The second parameter value storage unit 132 stores the value of the second parameter group output from the second parameter value calculation unit 122. The used car price data storage unit 136 stores used car price data. The used car price data storage unit 136 includes a used car price initial data storage unit (not shown) for storing used car price initial data. Note that the used car price initial data and used car price data in this embodiment are the same data as in the first embodiment.

  Next, the insurance premium calculation process in this embodiment will be described with reference to the flowchart shown in FIG. The insurance fee calculation apparatus 100 receives the used car price initial data by the input means 112 (step 40). An elapsed period and a residual value rate are calculated for each data from the received used car price initial data (step 42). Using the elapsed period and the residual value rate, the value of the first parameter group that defines the Weibull distribution is calculated based on the Weibull distribution model formula (step 44). A predicted residual value rate is calculated based on the Weibull distribution model equation using the calculated value of the first parameter group and displayed on a graph (step 46). Also, using the elapsed period and the residual value rate, the value of the second parameter group that defines the OU process is calculated based on the OU process model equation (step 48). Based on the calculated value of the second parameter group, the predicted value of the variance of the logarithmic value of the residual value rate is calculated based on the OU process model equation and displayed on the graph (step 50). Then, the insurance premium is calculated from the insurance premium calculation formula using the calculated value of the first parameter group and the value of the second parameter group (step 52).

  In the present embodiment, Step 40 to Step 50 are the same as those in the first embodiment described above. In step 52, by calculating the insurance premium using the calculated value of the first parameter group and the value of the second parameter group, the remaining value considering the basic value and market value of the used car is taken into account. Insurance premium calculation processing based on price prediction is possible.

  Next, the insurance premium calculation process shown in step 52 will be specifically described. Here, the initial residual value rate parameter value P determined by the processing shown in Steps 40 to 50, the calculated and determined values of the first parameters (α, β), and the calculated and determined second values. The premium is calculated from the premium calculation formula using the values of the parameters (θ, σ).

  Used car residual value guarantee insurance sets the contract residual value (residual value set at the time of lease contract) or the contract residual value rate, and if the actual used car residual value or the actual used car residual value ratio falls below this, The insurance pays insurance money according to the degree. In this embodiment, the insurance premium is calculated on an index basis. Here, the index is an average residual value rate of a plurality of vehicles, and the index base is a model for calculating insurance premiums for the average residual value rates of a plurality of vehicles.

Assuming that the number of used cars constituting the index is U, U is a discrete random variable that changes randomly every period. If the average value based on past data is λ, it can be said that the number of used cars U constituting the index follows a Poisson distribution with λ as a parameter. The upper and lower limits of the insurance premium are obtained by the following equations for the number of used cars U to Poisson (λ) and the independent identical distribution (iid) normal random variables Z _{n to} N (0, 1).

Here, the insurance premium is based on the assumption that a simple average value of actual data over a certain period is used as an index. Insurance premiums in this case can be formulated in a manner similar to the pricing of the arithmetic average price option often used for commodity derivatives. Here, since the processing is performed assuming that the used car residual value (rate) follows a lognormal distribution, it is difficult to derive the distribution that the arithmetic average follows. However, since it is possible to derive the distribution that the geometric mean follows, the above formula is approximated using the geometric mean.

Therefore, the premium calculation formula for obtaining the upper limit l of the premium expressed by the formula 41 is based on the relationship between the arithmetic mean and the geometric mean.
It is guided.

In addition, when calculating the expected value with geometric mean condition using Jansen's inequality, the opposite direction is obtained. Therefore, the premium calculation formula for obtaining the lower limit value l of the premium expressed by the formula 41 is as follows:

It is guided.

The input means 112 includes the value of the contract residual value K of the target vehicle, the value of the number U of index components, the value of the planned elapsed period (monthly) t of the target vehicle, the value of the planned interest rate r, the new vehicle price

Accepts the value of. Here, the values of k and γ are zero. The insurance fee calculation unit 128 receives these values received by the input means 112, the value of the initial residual value parameter p determined in the processing shown in steps 40 to 50, and the first parameter (α , Β) and the calculated and determined values of the second parameters (θ, σ), the upper and lower limit values l of the insurance premiums are calculated from the above formula.

[Other Embodiments]
The residual value rate prediction apparatus and insurance premium calculation apparatus according to the present invention are not limited to the above-described embodiments. In another embodiment, when the insurance premium calculation process is performed by the insurance premium calculation device, an insurance premium calculation formula assuming a case in which the risk of each vehicle is secured may be used. Used car residual value guarantee insurance is an insurance that sets a contract residual value (rate) and pays insurance money according to the degree when the actual residual value (rate) of used cars falls below this. Therefore, the insurance premium for used car residual value guarantee insurance is formulated in the same way as the option fee for European amput option with strike as the contract residual value K. Therefore, the insurance premium is calculated from the following equation. If the planned interest rate is r, the premium for residual value insurance is as follows:

In this formula, the probability of paying insurance is the coefficient in the first term.

The input means 112 includes the value of the contract residual value K of the target vehicle, the value of the planned elapsed period (monthly) t of the target vehicle, the value of the planned interest rate r, and the new vehicle price.

Accepts the value of. Here, the values of k and γ are zero. In addition, the insurance fee calculation unit receives these values received by the input means, the value of the initial residual value parameter p determined in the processing shown in Steps 40 to 50, and the first parameter (α that is calculated and determined) , Β) and the calculated and determined value of the second parameter (θ, σ), the insurance premium l is calculated from the above formula.

  Further, in the insurance fee calculation device, step 46 and step 50 may be omitted, and the optimum value is determined from a plurality of values of the first and second parameter groups calculated in step 44 and step 48. The insurance premium can be calculated using the values of the first and second parameter groups.

  In addition, it is a product that can express the residual value rate at a specific time point in a Weibull distribution, and the variance of the logarithmic value of the residual value rate follows an OU process in which the volatility converges to a constant value over time. As long as it is a product, the present invention can be realized even in second-hand goods other than used cars.

It is a block diagram of the residual value rate prediction apparatus in the 1st Embodiment of this invention. It is a flowchart which shows the flow of the residual value rate prediction process in the 1st Embodiment of this invention. It is a flowchart which shows the flow of the prediction residual value rate calculation process in the 1st Embodiment of this invention. It is a flowchart which shows the flow of the predicted value calculation process of the logarithm value dispersion | distribution of the residual value rate in the 1st Embodiment of this invention. It is a data output figure which shows an example of output data, such as a 1st parameter value, in the 1st Embodiment of this invention. It is a graph which shows an example of the output data in the 1st Embodiment of this invention. It is a data output figure which shows an example of output data, such as a 2nd parameter value, in the 1st Embodiment of this invention. It is a graph which shows an example of the output data in the 1st Embodiment of this invention. It is a block diagram of the insurance premium calculation apparatus in the 2nd Embodiment of this invention. It is a flowchart which shows the flow of the insurance premium calculation process in the 2nd Embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Residual value rate prediction apparatus 12 Input means 14 Calculation means 16 Storage means 20 1st parameter value calculation part 22 2nd parameter value calculation part 24 Prediction residual value rate calculation part 26 Distributed prediction value calculation part 30 1st parameter value Storage unit 32 Second parameter value storage unit 34 Used car price data storage unit 100 Insurance premium calculation device 112 Input unit 114 Calculation unit 116 Storage unit 120 First parameter value calculation unit 122 Second parameter value calculation unit 124 Prediction remaining Price calculation unit 126 Distributed prediction value calculation unit 128 Insurance premium calculation unit 130 First parameter value storage unit 132 Second parameter value storage unit 136 Used car price data storage unit

Claims (3)

Second-hand price data storage means for storing second-hand price data including residual value data, which is a ratio of second-hand goods price to new price, and elapsed time data of the second-hand goods;
Applying a Weibull distribution model formula to the used price data, calculating a value of a first parameter group that defines the Weibull distribution of the residual value rate, and outputting a first parameter value calculating means;
First parameter value storage means for storing the output value of the first parameter group;
Applying the Ornstein-Uhlenbeck process model formula to the used price data, calculating the value of the second parameter group that defines the Ornstein-Uhlenbeck process relating to the residual value rate, and outputting the value Parameter value calculation means;
Second parameter value storage means for storing the value of the output second parameter group;
Using the value of the first parameter group that has been calculated and stored, the predicted residual value ratio of the second-hand goods is calculated based on the Weibull distribution, and the predicted residual value ratio is output. Means,
The variance for calculating the predicted value of the variance of the logarithmic value of the residual value rate based on the Ornstein-Uhlenbeck process using the value of the calculated and stored second parameter group and outputting the predicted value A residual value rate prediction apparatus comprising: a predicted value calculation unit. Second-hand price data storage means for storing second-hand price data including residual value data, which is a ratio of second-hand goods price to new price, and elapsed time data of the second-hand goods;
Applying a Weibull distribution model formula to the used price data, calculating a value of a first parameter group that defines the Weibull distribution of the residual value rate, and outputting a first parameter value calculating means;
First parameter value storage means for storing the output value of the first parameter group;
Applying the Ornstein-Uhlenbeck process model formula to the used price data, calculating the value of the second parameter group that defines the Ornstein-Uhlenbeck process relating to the residual value rate, and outputting the value Parameter value calculation means;
Second parameter value storage means for storing the value of the output second parameter group;
An insurance premium comprising: insurance premium calculating means for calculating an insurance premium using the value of the stored first parameter group and the value of the stored second parameter group and outputting the insurance premium Calculation device.   The insurance premium calculation apparatus according to claim 2, wherein the insurance premium calculation means performs calculation using an insurance premium calculation formula.