JP4974097B2 - Credit issuer calculation system and calculation program for bond issuers - Google Patents

Description

  The present invention relates to a bond issuer's creditworthiness calculation system and calculation program, and in particular, based on the market price (current price) of a bond belonging to a specific issuer, (Technology for calculating default).

Financial institutions such as banks and institutional investors such as insurance companies need to know in advance the default probability of the borrower or investee company in order to diversify the risk. Based on this, the probability of bankruptcy has been roughly grasped.
However, credit information from rating agencies has the following problems.
(1) Renewal is slow because it takes time to interview the target company.
(2) Evaluation criteria and information sources are unclear and poor in objectivity. As a result, there are many cases where evaluations are largely divided between each affiliated company.
(3) The number of target companies by one rating company is limited to several hundred.

  On the other hand, in Patent Document 1, the price of a bond, which is a borrowing statement of a company's debt, is assumed to include a market evaluation regarding the probability of bankruptcy of the issuing company. A technique for calculating the creditworthiness of a company by comparing with the price and attributes of government bonds that are extremely close to zero is disclosed.

JP 2001-125953 A

As claimed by the inventor in Patent Document 1, there remains a question as to whether the default recovery rate information is incorporated in bond prices, but at least traders trade in bond transactions based on the credit risk of the issuer. Since the price is set, the idea of estimating creditworthiness based on bond prices can be supported.
In this way, calculating creditworthiness based on public information such as the market price of bonds provides objective judgment results compared to credit information provided by traditional rating agencies, and provides credit for a wider range of issuers. The force can be calculated.

However, a large number of bonds are not necessarily issued from a single issuer, and there are many cases where the basic data for calculating the creditworthiness period structure for each individual company is insufficient.
For this reason, Patent Document 1 basically adopts a technique for deriving creditworthiness in each industry by inputting bond information of a large number of companies and analyzing them in each industry. Each company's creditworthiness is calculated by applying weight information for each industry (for example, 30% for fisheries, 70% for manufacturing, etc.) to the creditworthiness of each industry.
That is, in Patent Document 1, since the basic data for analyzing the period structure is insufficient for each individual company, the network is expanded to the industry level and a large amount of bond information is sampled. After obtaining the information, the method of deriving the creditworthiness of each individual company based on the industry structure of the target company is adopted.
For this reason, even if a large group such as “industry” may lead to a relatively reliable value, the industry structure (weight of industry) of each company is vague and subjective. In addition, there is a problem that the creditworthiness of each individual company that institutional investors really need is not reliable.

  The present invention has been devised in view of the above-described problems associated with the calculation of corporate creditworthiness, and an object thereof is to provide a technique capable of calculating the creditworthiness at an individual company level with high accuracy.

In order to achieve the above-mentioned purpose, the creditworthiness calculation system for a bond issuer described in claim 1 includes a maturity date for one or more bonds belonging to a specific issuer, a yield of the bond, and a yield of a government bond. Input means for inputting a spread representing the difference between the bond, the maturity date of each bond, means for storing the spread of each bond in the spread / attribute information storage unit, and interpolating the spread belonging to each issuer Thus, a spread curve generating means for generating a spread curve for estimating a term structure of a bond remaining age and a spread in a specific issuer, and a spread at a specific remaining age on the spread curve are extracted, and this is extracted. and discount bonds based spreads converting means for converting the discount bonds based spreads, to assign the discount bond based spreads to a predetermined formula By calculates the default probability at a specific maturity time of the issuer, means for storing the calculation result storage unit, processes the default probabilities stored in the calculation result storage unit into a predetermined format, display or The spread curve generating means includes a means for outputting to a printer, wherein the spread curve generating means has a stock of bonds belonging to a specific issuer exceeding a predetermined number, and the distribution of each remaining period exceeds a predetermined period. If it is distributed, a process of generating a curved spread curve by logarithmic interpolation is executed, and there are a predetermined number of bonds belonging to a specific issuer, and the distribution of each remaining period exceeds the predetermined period. If it is distributed, execute a process to generate a linear spread curve with a slope by linear interpolation, and belong to a specific issuer Regardless of the number of issues of the ticket, if the distribution of each remaining period is concentrated within a predetermined period, a process is performed to generate a straight spread curve with no slope by constant interpolation, and the above discount The bond-based spread conversion means obtains a value at a predetermined remaining age on the spread curve and assigns this value to a predetermined formula to calculate a yield at each remaining age, and Execute the process of calculating the discount factor at each remaining age by substituting it into a predetermined formula, and the process of calculating the discount bond base spread at each remaining age by substituting this discount factor into the predetermined formula It is characterized by.

In addition, the creditworthiness calculation program for a bond issuer described in claim 2 uses a computer to calculate the difference between the maturity date of one or more bonds belonging to a specific issuer and the yield of the bond and the yield of government bonds. Input means for inputting a spread representing the maturity date of each bond, means for storing the spread of each bond in the spread / attribute information storage unit, and by interpolating the spread belonging to each issuer , a specific Spread curve generation means for generating a spread curve that estimates the term structure between the bond's remaining years and spread in the issuer, and extracts the spread at the specified remaining years on the spread curve and converts it to a discount bond base spread discount notes-based spreads converting means for, in substituting the said discount bonds based spreads to a predetermined formula Calculates the default probability at a specific maturity time of the issuer, the calculation result means for storing in the storage unit, processes the default probabilities stored in the calculation result storage unit into a predetermined format, output to a display or printer The spread curve generating means has a bond issuer belonging to a specific issuer exceeding a predetermined number, and the distribution of each remaining period is distributed over a predetermined period. If there is a fixed number of bonds that belong to a specific issuer, the distribution of each remaining period is distributed over a predetermined period. If there is a bond that belongs to a specific issuer, it executes a process to generate a linear spread curve with a slope by linear interpolation. Regardless of the number of issues, if the distribution of each remaining period is concentrated within a predetermined period, a process of generating a straight spread curve with no slope by constant interpolation is executed, The base spread conversion means obtains a value at a predetermined remaining age on the spread curve and assigns this value to a predetermined mathematical formula to calculate a par yield at each remaining age, By substituting the discount factor for each remaining age by substituting it into the formula, and executing the processing for calculating the discount bond base spread at each remaining age by substituting this discount factor into a predetermined formula It is a feature.

In the bond issuer's creditworthiness calculation system and calculation program according to the present invention, the creditworthiness of the issuer is calculated based on a spread representing the difference between the yield of the bond and the yield of the government bond. This makes it possible to immediately present more objective information on corporate credit risk.
Moreover, since the spread curve is estimated by mathematically interpolating the spread of each issue, even if the number of issues of bonds belonging to the target company is small, it does not refer to other companies' information. The default probability for any remaining years can be directly calculated.

FIG. 1 is a block diagram showing a functional configuration of a bond issuer creditworthiness calculation system 10. An input device 12 such as a keyboard and a mouse, a spread / attribute information registration unit 14, a spread / attribute information storage unit 16, A calculation processing unit 18, a calculation result storage unit 20, a calculation result output unit 22, a display 24, and a printer 26.
The spread / attribute information registration unit 14, the calculation processing unit 18, and the calculation result output unit 22 are realized by the CPU of the computer (PC, etc.) 28 executing necessary processes according to the OS and a dedicated application program. The
The spread / attribute information storage unit 16 and the calculation result storage unit 20 are provided in a hard disk or a memory of the computer 28.

Next, a processing procedure in the system 10 will be described according to the flowchart of FIG.
First, the operator inputs, as basic data for calculating creditworthiness, via the input device 12, attribute information such as the issue spread of issued bonds and the maturity date of each issue for each issuer of bonds (S10).
Here, the spread represents the difference between the yield of the bond and the yield of government bonds. JGBs are bonds with no credit risk, so the larger the spread, the better the yield, but the higher the credit risk.
The input spread information and attribute information are converted into a necessary format by the spread / attribute information registration unit 14, and then stored in the spread / attribute information storage unit 16 (S12).

この問題は、log(t＋1)を一つの変数Tとみると、単なる最小二乗法に帰着できることがわかる。このため、a_k, b_kは以下の数２のように計算できる。

この際、最小二乗法の精度を表す指標として、R_k ²の値も以下の数３のように算出する。

以上の結果、図４に示すように、演算処理部18によって各銘柄のスプレッドに基づくスプレッドカーブが生成される。 Next, the arithmetic processing unit 18 is activated, and the creditworthiness of the issuer is calculated based on the input bond spread.
At this time, the arithmetic processing unit 18 determines the distribution of the number of issues of the bond and the remaining years calculated from the respective maturity dates (S14), and executes different processes depending on the determination result.
That is, as shown in FIG. 3, when the distribution range of the remaining years of each issue belonging to an issuer k is 2 years or more and the issue number is 3 or more, the spread of each issue is logarithmically interpolated. Thus, a spread curve of issuer k is generated (S16).
Specifically, a _k and b _k in Equation 1 below are estimated.

When log (t + 1) is regarded as one variable T, this problem can be reduced to a simple least square method. For this reason, a _k and b _k can be calculated as shown in Equation 2 below.

At this time, as an index representing the accuracy of the least squares method, the value of R _k ² is also calculated as shown in Equation 3 below.

As a result, as shown in FIG. 4, a spread curve based on the spread of each brand is generated by the arithmetic processing unit 18.

By the way, corporate bonds are accompanied by coupons (interest), and it is considered that the spread curve obtained above contains credit information for coupons generated periodically (many every six months).
Therefore, the arithmetic processing unit 18 extracts a spread at a specific time from the spread curve (S18), and executes a process of converting the spread into a discount bond (zero coupon bond) based spread in which no coupon is generated.

For example, as shown in FIG. 5, as a specific point in time when the spread is extracted, the remaining years are 0.25 years, 0.5 years, 1.0 years, 1.5 years, 2.0 years, 2.5 years, 3.0 years, 3.5 years, 4.0 years, 4.5 years, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10.0
i: Time grid number (i = 1, ..., 21)
t _i : Time grid
・ T ₁ = 0.25
・ When i ≧ 2, t ₁ = 0.5 * (i−1)
And it is defined, the method of estimating the discount bonds based spread of the remaining years t _N year is as follows.
First, when N = 1 (that is, the remaining age of 0.25 years), the spread of the remaining years of 0.25 years in the spread curve in FIG.
On the other hand, when N ≧ 2, the processing unit 18 calculates a discount bond-based spread for each remaining years by executing the following processes.

この数式を解くことにより、以下の数５に示すように、パーイールドx_k,Nが求まる。

[Calculation of per-yield (based on half-year compound interest)]
First, from the spread s _{k, i} of the remaining years t _i of the issuer _k, a per yield (half year compound interest basis) x _{k, N} is obtained (S20).
That is, the following equation 4 is derived from the definition of par yield.

By solving this mathematical formula, the per-yield x _{k, N} is obtained as shown in the following equation (5).

つぎに、i＝3（残存年数1.0年）とした場合も、パーイールドの定義により、以下の数７に示す通りE_k,3が求められる。

i≧4以降も同様にパーイールドの定義に従い、以下の数８に示す通りE_k,4〜E_k,2Nが求められる。

[Calculation of discount factor]
Next, the arithmetic processing unit 18 obtains a discount factor E _{k, N} of the issuer k from the par yield x _{k, N} of the issuer k (S22).
First, when i = 2 (remaining years 0.5 years), E _{k, 2} is obtained as shown in the following equation 6 according to the definition of par yield.

Next, even when i = 3 (remaining years 1.0), E _{k, 3} is obtained as shown in the following equation 7 by the definition of par yield.

Similarly, after i ≧ 4, E _{k, 4 to} E _{k, 2N} are obtained as shown in the following equation 8 according to the definition of par yield.

[Calculation of discount bond base spread]
Next, the arithmetic processing unit 18 calculates the discount bond base spread S ′ _{k, i} of the remaining years t _i of the issuer k from the discount factor E _N of the remaining years t _i of the issuer k (S24).
That is, the following equation 9 is established from the definition of spread, and by developing this, a discount bond base spread is obtained as shown in equation 10.

[Calculation of cumulative default probability]
Finally, the arithmetic processing unit 18 by substituting discount bonds based spreads S _'k of maturity t _i year issuers k obtained _above, the _i in the following equation 11, after t _i years issuers k The cumulative default probability (risk neutral basis) is obtained (S26) and stored in the calculation result storage unit 20 (S28).

The default probability stored in the calculation result storage unit 20 by the arithmetic processing unit 18 is processed into a predetermined format by the calculation result output unit 22, and then output to the outside through the display 24 and the printer 26 (S30).
FIG. 6 shows a display example of discount bond base spread in each grid and the accumulated default probability calculated based on the spread.

この場合、a_k, b_kは以下の数１３のように計算できる。

この場合も、最小二乗法の精度を表す指標として、上記の数３を用いてR_k ²の値が算出される。
以上の結果、図７に示した通り、演算処理部18によって傾きを有する直線状のスプレッドカーブが生成される。 As shown in FIG. 7, when the distribution range of the remaining years of each bond issue belonging to the issuer k is two years or more and the number of issues is two, the arithmetic processing unit 18 linearly interpolates between the spreads of each issue. Thus, a spread curve of the issuer k is generated (S32).
Specifically, a _k and b _k in Equation 12 below are estimated.

In this case, a _k and b _k can be calculated as shown in Equation 13 below.

Also in this case, the value of R _k ² is calculated using Equation 3 as an index representing the accuracy of the least square method.
As a result, as shown in FIG. 7, a linear spread curve having an inclination is generated by the arithmetic processing unit 18.

  Thereafter, the arithmetic processing unit 18 executes the above-described processes of S18 to S26 to extract a spread at a predetermined time point, convert it to a discount bond base, and then substitute it into Equation 11 until a specific time point. Compute the cumulative default probability for issuer k of.

以上の結果、図８に示した通り、演算処理部18によって直線上のスプレッドカーブが生成される。 As shown in FIG. 8, when the distribution range of the remaining years of bond issues belonging to issuer k is less than 2 years, it is difficult to estimate the slope of the spread curve because there is no significant difference in the yield of each issue. Therefore, regardless of the number of issues, the arithmetic processing unit 18 generates a spread curve of the issuer k as a constant function of the average value of each spread (S34).
Specifically, a _k and b _k are calculated as in the following equation 14 based on the above equation 12.

As a result, as shown in FIG. 8, a straight spread curve is generated by the arithmetic processing unit 18.

  In this case, the spreads at the respective time points are equal, but the arithmetic processing unit 18 converts the spreads into discount bond-based spreads using the above-described method, and then substitutes them into Equation 11 to calculate the default probability of the issuer k. .

It is a block diagram which shows the function structure of the creditworthiness calculation system of a bond issuer. It is a flowchart which shows the process sequence in this system. It is a graph which shows the case where the distribution range of the remaining years of the bond which belongs to a specific issuer is 2 years or more, and the number of issues is 3 or more. It is a graph which shows a spread curve in case the distribution range of the remaining years of the bond which belongs to a specific issuer is 2 years or more, and the number of issues is 3 or more. It is a graph which shows a mode that the spread in the specific time on a spread curve is extracted. It is a graph which contrasts discount bond base spread and cumulative default probability. It is a graph which shows a spread curve in case the distribution range of the remaining years of the bond which belongs to a specific issuer is 2 years or more, and the number of issues is 2. It is a graph which shows a spread curve in case the distribution range of the remaining years of the bond which belongs to a specific issuer is less than 2 years.

10 Bond issuer creditworthiness calculation system
12 Input device
14 Spread / attribute information registration section
16 Spread / attribute information storage
18 Arithmetic processing section
20 Calculation result storage
22 Calculation result output section
24 display
26 Printer
28 computers

Claims (2)

An input means for inputting a maturity date of one or more bonds belonging to a specific issuer and a spread representing a difference between a yield of the bond and a yield of the government bond;
Means for storing the maturity date of each bond entered and the spread of each bond in the spread / attribute information storage unit;
A spread curve generating means for generating a spread curve for estimating a term structure of a bond remaining age and a spread in a specific issuer by interpolating the spread belonging to each issuer;
A discount bond based spread conversion means for extracting a spread at a specific remaining age on the spread curve and converting the spread into a discount bond base spread ;
By substituting the discount bond base spread into a predetermined mathematical formula, a default probability at a specific remaining years of the issuer is calculated and stored in a calculation result storage unit ;
A bond issuer creditworthiness calculation system comprising means for processing the default probability stored in the calculation result storage unit into a predetermined format and outputting the result to a display or a printer,
The above spread curve generating means uses a logarithmic interpolation to calculate a curve-like shape when the number of bonds belonging to a specific issuer exceeds a predetermined number and the distribution of each remaining period exceeds a predetermined period. When processing to generate a spread curve is executed and there are a predetermined number of bonds belonging to a specific issuer and the distribution of each remaining period is distributed over a predetermined period, the slope is determined by linear interpolation. If the distribution of each remaining period is concentrated within a given period regardless of the number of issues of bonds belonging to a specific issuer, constant interpolation is performed. Execute the process to generate a straight spread curve without slope,
The discount bond base spread conversion means obtains a value at a predetermined remaining age on the spread curve and assigns the value to a predetermined formula to calculate a yield at each remaining age, Execute the process of calculating the discount factor at each remaining age by substituting the yield into a predetermined formula and the process of calculating the discount bond base spread at each remaining age by substituting this discount factor into the predetermined formula creditworthiness calculation system of bond issuers, characterized by. Computer
An input means for inputting a maturity date of one or more bonds belonging to a specific issuer and a spread representing a difference between the yield of the bond and the yield of the government bond,
Means for storing the maturity date of each bond and the spread of each bond in the spread / attribute information storage unit;
A spread curve generating means for generating a spread curve for estimating a term structure of a bond remaining age and a spread in a specific issuer by interpolating the spread belonging to each issuer;
A discount bond based spread conversion means for extracting a spread at a specific remaining age on the spread curve and converting the spread into a discount bond base spread ;
Means for calculating a default probability at a specific remaining years of the issuer by substituting the discount bond base spread into a predetermined formula, and storing it in a calculation result storage unit;
This is a bond issuer creditworthiness calculation program that processes the default probability stored in the calculation result storage unit into a predetermined format and functions as a means for outputting to a display or printer,
The above spread curve generating means uses a logarithmic interpolation to calculate a curve-like shape when the number of bonds belonging to a specific issuer exceeds a predetermined number and the distribution of each remaining period exceeds a predetermined period. When processing to generate a spread curve is executed and there are a predetermined number of bonds belonging to a specific issuer and the distribution of each remaining period is distributed over a predetermined period, the slope is determined by linear interpolation. If the distribution of each remaining period is concentrated within a given period regardless of the number of issues of bonds belonging to a specific issuer, constant interpolation is performed. Execute the process to generate a straight spread curve without slope,
The discount bond base spread conversion means obtains a value at a predetermined remaining age on the spread curve and assigns the value to a predetermined formula to calculate a yield at each remaining age, Execute the process of calculating the discount factor at each remaining age by substituting the yield into a predetermined formula and the process of calculating the discount bond base spread at each remaining age by substituting this discount factor into the predetermined formula A creditworthiness calculation program for bond issuers characterized by

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