JP2007264939A - Pricing system and pricing program for enterprise debt - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide technology allowing rapid and objective calculation of a market price of an enterprise debt wherein a market interest rate is absent. <P>SOLUTION: This pricing system 10 for the enterprise debt has: a basic information storage part 16 storing residual periods of a plurality of public issues, a spread showing a difference between a return of each the public issue and a return of a government bond, a business category code of an issuing enterprise of each the public issue, and specific financial data related to each the issuing enterprise; a regression model generation part 18 executing regression analysis with the residual period and the financial data as an explanatory variable of the spread in each the same business category, deriving a regression model, and storing it into a regression model storage part 20; an input device 12 for inputting the residual period, the business category code of the enterprise, and the financial data of the enterprise with respect to a loan of the specific enterprise; a spread calculation part 22 applying the residual period of the loan and the financial data of the enterprise to the regression model related to the business category of the enterprise to calculate the spread of the loan, and thereafter converting it into the discount bond-based spread; and a calculation result output part 26 outputting it onto a display 28. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a corporate debt pricing system and a pricing program, and more particularly to a technique for calculating an appropriate price for a loan of a publicly issued bond unissued company or a private placement bond.

In recent years, corporate debts such as corporate loans that do not have a market interest rate have been attracting attention as transactions, and there has been a demand for more sophisticated risk management. However, there is an urgent need in financial institutions.
Here, since it is generally considered that credit risk reflects the credit risk to bond issuers, if a company issues publicly offered bonds, the price of loans and private placement bonds is estimated based on the market interest rate. However, the number of companies that issue publicly offered bonds is limited, and the fact is that there is no objective measure for creditworthiness such as market interest rates for the majority of companies. is there.

In order to solve this problem, Patent Document 1 uses a statistical method to derive a relational expression between the market interest rate of a highly rated company that issues publicly offered bonds, the remaining period of bonds and the cumulative bankruptcy probability by rating. In addition, a technique for estimating an appropriate yield is disclosed by applying the debt remaining period of a low-rated company and the cumulative bankruptcy probability by rating to this relational expression.
JP-A-2005-174309

However, since the technology of this patent document 1 is the one that realizes the pricing of corporate debts on a rating unit basis, the value becomes discrete, and the accuracy of the interest rate calculation method for marketable products is insignificant or coarse. I don't get it.
In addition, the rating of a company may be slow to update, and there is a possibility that the allegations of a rating agency may be mixed in, so it may not be possible to obtain a fresh and objective result.

  The present invention has been devised in view of the above-mentioned problems relating to pricing of corporate debts, and can quickly and objectively determine the market price of corporate debts that do not have market interest rates without depending on the rating of the firm. The purpose is to provide computable technology.

  In order to achieve the above-mentioned object, the corporate debt pricing system according to claim 1 includes a plurality of publicly issued bonds with a remaining period, a spread indicating a difference between a yield of each publicly offered bond and a yield of a government bond, and each publicly issued bond. Storage means for storing specific financial data relating to the issuer of the company, means for deriving a regression model by performing regression analysis using the remaining period and financial data as explanatory variables of the spread, and regression of the regression model The means for storing in the model storage means, the remaining period of the liability of the specific company, the means for inputting the same kind of financial data as for the company, and the remaining period of the liability and the company for the regression model And means for calculating a spread of the debt by applying financial data.

  In addition, the corporate debt pricing system described in claim 2 includes the remaining periods of multiple publicly offered bonds, spreads representing the difference between the yield of each publicly offered bond and the yield of government bonds, and the industry code of the company issuing each publicly offered bond Storage means for storing specific financial data relating to each issuing company, means for deriving a regression model by performing regression analysis with the remaining period and financial data as explanatory variables of the spread for each same industry , Means for storing the regression model for each industry in the regression model storage means, means for inputting the remaining period, the industry code of the company, and the same type of financial data relating to the company with respect to the liability of the specific company And a means for extracting a regression model relating to the industry of the company from the regression model storage means, and applying the remaining period of the liability and the financial data relating to the company to the regression model. By, it is characterized by comprising means for calculating the spread of the debt.

  Further, the corporate debt pricing system according to claim 3 is the system according to claim 1 or 2, further comprising means for converting the spread of the debt into a discount bond-based spread. .

  In addition, the corporate debt pricing program described in claim 4 uses a computer, a remaining period of a plurality of publicly offered bonds, a spread representing the difference between the yield of each publicly offered bond and the yield of a government bond, and the issuance of each publicly issued bond. Storage means for storing specific financial data relating to a company, means for executing regression analysis using the remaining period and financial data as explanatory variables of the spread, and deriving a regression model, and storing the regression model in the regression model storage means Means for storing, means for inputting the remaining period of the liability of a specific company and financial data of the same type as for the company, applying the remaining period of the liability and the financial data of the company to the regression model Therefore, it is made to function as a means for calculating the spread of the debt.

  According to the corporate debt pricing system as set forth in claim 1 and the pricing program as set forth in claim 4, based on various financial data indicating the safety and profitability of the company, the loans and private bonds of non-publicly issued bonds Since the market interest rate is calculated, there is an advantage that a continuous and appropriate value can be obtained.

  In the case of the corporate liability pricing system described in claim 2, since a regression model for each industry is derived and a regression model corresponding to the industry of the company is applied when calculating the spread of the company debt, Pricing that reflects these characteristics is possible.

  According to the corporate debt pricing system described in claim 3, since a spread converted to a discounted bond is obtained, an advantage of obtaining a more accurate price excluding credit information for coupons (interest) of publicly offered bonds There is.

FIG. 1 is a block diagram showing a functional configuration of a corporate debt pricing system 10 according to the present invention, which includes an input device 12, such as a keyboard and a mouse, an input information registration unit 14, a basic information storage unit 16, and a regression model. A generation unit 18, a regression model storage unit 20, a target loan information storage unit 21, a spread calculation unit 22, a calculation result storage unit 24, a calculation result output unit 26, a display 28, and a printer 30 are provided. Yes.
The input information registration unit 14, the regression model generation unit 18, the spread calculation unit 22, and the calculation result output unit 26 described above are executed by the CPU of the computer (PC, etc.) 32 according to the OS and a dedicated application program. It is realized by doing.
The basic information storage unit 16, the regression model storage unit 20, the target loan information storage unit 21, and the calculation result storage unit 24 are provided in a hard disk or a memory of the computer 32.

  As shown in FIG. 2, the system 10 processes spread 44, which is the difference between the market interest rate 40 of each publicly offered bond and the government bond rate 42, the remaining years 46 of each publicly offered bond, and the financial data of each publicly issued bond issuer. By statistically processing 48 for each industry, a phase of generating a regression model 50 for each industry, and substituting the remaining years 52 of loans related to non-issued corporate bonds and financial data 54 of the company into this regression model 50 Therefore, the loan spread (based on discounted bonds) 56 is derived, and the interest rate 58 of the loan is derived by combining it with the government bond interest rate 42.

Hereinafter, a specific processing procedure in the system 10 will be described with reference to the flowchart of FIG.
First, the operator inputs a large number of patterns of combinations of basic information including the issuing company code of the publicly offered bond issuer, the industry code, various financial data, the issue code of the publicly offered bond, the spread, and the remaining years via the input device 12 (S10 ).

  As mentioned above, the spread represents the difference between the yield of publicly offered bonds and the yield of government bonds. JGBs can be regarded as bonds with no credit risk, so the larger the spread, the better the yield, but the higher the credit risk.

In addition, as the above-described financial data, for example, indicators that strongly indicate the safety (risk) and profitability of the company, such as the total asset amount of the company, the capital adequacy ratio, and the total return on capital, are selected.
This financial data is specifically selected through the following procedure.
(1) List a large number of financial data as candidates.
(2) The companies that existed at a certain point in time in the past (time A) are classified into companies that have been defaulted and those that have not been defaulted.
(3) From the financial data of each company at time A, select a predetermined number that greatly differs between the default group and the non-default group.
Evaluation of this difference is judged by using as an index the difference between the average values of each group divided by the standard deviation of the default group.

The input basic information is converted into a necessary format by the input information registration unit 14, and then stored in the basic information storage unit 16 (S12).
Instead of inputting basic information via the input device 12, a basic information file shaped into a predetermined format is stored in a recording medium such as a memory card, and the basic information storage unit 16 is connected via a reader. You may make it store in.

Next, the regression model generation unit 18 is activated, and performs the multiple regression analysis for each industry by using the input remaining years of each publicly offered bond and the financial data of the publicly issued bond issuing company as explanatory variables, and the spread as an objective variable, A regression model (proportional hazard model) for each industry is derived (S14).
Specifically, by generating a number of samples by substituting the spread, remaining years, and financial data for each publicly offered bond in the regression equation (relational equation) and performing regression analysis on these samples, λ (constant term) , Γ (regression coefficient of remaining years), β _i (regression coefficient of each financial data) are estimated. Equation 1 shows an example of the regression equation.

FIG. 4 is a table exemplifying a calculation result when using the regression equation of Equation 1, and λ (constant term), γ (remaining years) for each industry of “material”, “transport”, and “automobile”. ), Β _{1 to} β _n (regression coefficient of each financial data) are stored.
In addition, the closer the value of “R-Square” (multiple coefficient of determination) is to 1, the better the correlation between items, and the higher the accuracy of prediction in multiple regression analysis, but relatively good for each industry It can be evaluated that the correct numerical value is derived.
The values of λ, γ, and β _i are stored in the regression model storage unit 20 by the regression model generation unit 18 for each business type (S16).

Next, the operator inputs, via the input device 12, the business type code of the specific publicly issued bond non-issuing company, the remaining loan years, and the same kind of financial data as above to the system 10 (S18).
The input information related to the target loan is converted into a necessary format by the input information registration unit 14, and then stored in the target loan information storage unit 21 (S19).
Thereafter, the spread calculation unit 22 is activated, and a regression model (combination pattern of λ, γ, β _i ) corresponding to the type of business of the company is extracted from the regression model storage unit 20 (S20).
Next, the spread calculation unit 22 calculates the remaining loan age in t of equation 1, z _ik , each financial data, λ a constant term, γ a remaining year regression coefficient, and β _i for each financial data. By substituting the regression coefficient, the spread S _k (t) of the corporate loan is calculated (S22).

By the way, corporate bonds are accompanied by coupons (interest), and it is considered that the spread obtained above contains credit information for coupons that are generated regularly (many every six months).
For this reason, the spread calculation unit 22 executes a process of converting the spread into a spread based on a discount bond (zero coupon bond) where no coupon is generated.

First, the remaining years are 0.25, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, Assuming 7.5, 8.0, 8.5, 9.0, 9.5, 10.0 years…
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, in the case of N = 1 (that is, the remaining age of 0.25 years), coupons are no longer generated, so the spread calculated above is used as the discount bond-based spread as it is.
On the other hand, when N ≧ 2, the spread calculation unit 22 calculates a spread based on discount bonds corresponding to the remaining years by executing the following processes.

この数式を解くことにより、以下の数３に示すように、パーイールドx_k,Nが求まる。

[Calculation of per-yield (half year compounded basis)]
First, a per-yield (half year compound interest basis) x _{k, N} is _obtained from the spread s _{k, i} of the loan remaining life t _i of the company k (S24).
That is, the following equation 2 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 (3).

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５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６に示す通りE_k,4〜E_k,2Nが求められる。

[Calculation of discount factor]
Next, the spread calculating unit 22 obtains a discount factor E _{k, N} of the company k from the par yield x _{k, N} of the company k (S26).
First, when i = 2 (remaining years 0.5 years), E _{k, 2} is obtained as shown in the following equation 4 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 5 by the definition of par yield.

Similarly, after i ≧ 4, E _{k, 4 to} E _{k, 2N} are obtained in accordance with the definition of par yield, as shown in the following equation (6).

[Calculation of discount bond base spread]
Next, the spread calculation unit 22 calculates the discount bond base spread S ′ _{k, i} of the loan remaining years t _i of the company k from the discount factor E _N of the remaining years t _i of the company k (S28).
That is, the following equation 7 is established from the definition of spread, and by developing this, a discount bond base spread is obtained as shown in equation 8.

Finally, the spread calculation unit 22 stores the calculated discount bond base spread in the calculation result storage unit 24 (S30).
The discount bond base spread is processed into a predetermined format by the calculation result output unit 26, and then output to the outside through the display 28 and the printer 30 (S32).
By adding this discount bond base spread to the current government bond interest rate, the appropriate interest rate of the corporate loan can be estimated.
In addition, by recalculating based on the latest data, the appropriate interest rate of the corporate loan can be updated at any time.

It is a block diagram which shows the function structure of the pricing system of a corporate debt. It is a schematic diagram for outlining the processing content in this system. It is a flowchart which shows the specific process sequence in this system. 6 is a table illustrating the calculation results of λ, γ, and β _i in Equation 1.

Explanation of symbols

10 Corporate debt pricing system
12 Input device
14 Input information registration section
16 Basic information storage
18 Regression model generator
20 Regression model storage
21 Purpose loan information storage
22 Spread calculation section
24 Calculation result storage
26 Calculation result output section
28 display
30 Printer
32 computers
40 Market interest rate on publicly offered bonds
42 Government bond interest rate
44 spreads
46 Remaining years of publicly offered bonds
48 Financial data of companies that issue publicly offered bonds
50 Regression model by industry
52 Loan remaining years
54 Financial data of non-publicly issued bonds
58 Appropriate interest rate on the loan

Claims (4)

A storage means for storing a remaining period of a plurality of publicly offered bonds, a spread representing a difference between a yield of each publicly issued bond and a yield of a government bond, and specific financial data relating to a company issuing each publicly offered bond;
Means for performing regression analysis with the remaining period and financial data as explanatory variables of the spread, and deriving a regression model;
Means for storing the regression model in the regression model storage means;
With regard to the liability of a specific company, the remaining period and means for inputting the same kind of financial data as above for the company,
Means for calculating the spread of the liability by applying the remaining period of the liability and the financial data of the company to the regression model;
A corporate debt pricing system characterized by comprising: Memory that stores the remaining periods of multiple publicly offered bonds, spreads representing the difference between the yield of each publicly offered bond and the yield of government bonds, the industry code of the issuing company of each publicly offered bond, and specific financial data relating to each issuing company Means,
A means for deriving a regression model by performing a regression analysis using the remaining period and financial data as explanatory variables of the spread for each same industry,
Means for storing the regression model for each industry in the regression model storage means;
With regard to the liability of a specific company, means for entering the remaining period, the industry code of the company, and the same kind of financial data as above for the company,
Means for extracting a regression model relating to the industry of the company from the regression model storage means;
Means for calculating the spread of the liability by applying the remaining life of the liability and the financial data of the company to the regression model;
A corporate debt pricing system characterized by comprising:   3. The corporate debt pricing system according to claim 1, further comprising means for converting the spread of the debt into a spread of discount bonds. Computer
A storage means for storing the remaining periods of a plurality of publicly offered bonds, a spread representing a difference between a yield of each publicly offered bond and a yield of a government bond, and specific financial data relating to a company issuing each publicly offered bond;
Means for performing regression analysis using the remaining period and financial data as explanatory variables of the spread, and deriving a regression model;
Means for storing the regression model in the regression model storage means;
With regard to the liability of a specific company, the remaining period and means for entering the same kind of financial data as above for the company,
Means for calculating the spread of the liability by applying the remaining period of the liability and the financial data of the company to the regression model;
A corporate debt pricing program characterized by its function as

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