JP2018013948A - Capital imposition calculation system and capital imposition calculation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To calculate capital imposition according to a standard system in FRTB and allow a change of capital imposition to be efficiently learned in the case of removing one or more specific transactions from a possessed portfolio.SOLUTION: A capital imposition calculation system includes: a sensitivity calculation unit 12 for calculating a calculation element including sensitivity to each risk factor according to a restriction requirement in a standard system for each trading transaction and recording it in a sensitivity DB 51; a capital imposition calculation unit 13 for calculating first capital imposition according to the restriction requirement on the basis of the calculation element recorded in the sensitivity DB 51 and recording it in a capital imposition DB 52; and a capital imposition change analysis unit 14 for calculating a change from the first capital imposition of second capital imposition when a removal transaction is removed and recording it in a change analysis result DB 53. The capital imposition change analysis unit 14 obtains a calculation element necessary at a time of calculating the second capital imposition by removing a part related to the removal transaction from the calculation element recorded in the sensitivity DB 51.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a risk management technique of a financial institution, and in particular, is applied to a capital charge calculation system and a capital charge calculation method for calculating a capital charge for a market risk of a trading account based on capital regulations by the Basel Committee on Banking Supervision. It relates to effective technology.

  In December 2014, the Basel Committee on Banking Supervision conducted “Fundamental Review of the Trading Book (FRTB)” as a strengthening of regulations on financial institutions (Non-Patent Document 1). (See Non-Patent Documents 2 and 3). Here, as a comprehensive review of the risk asset evaluation method for trading transactions at financial institutions, the regulations relating to the calculation method of capital charge (internal model method and standard method) for trading accounts are revised. Financial institutions such as banks, securities companies, and trust banks need to calculate the capital charge for trading accounts based on the revised regulations.

"Consultative Document, Fundamental review of the trading book: outstanding issues", [online], December 2014, Basel Committee on Banking Supervision, [searched July 11, 2016], Internet <URL: http: // www .bis.org / bcbs / publ / d305.pdf> "STANDARDS, Minimum capital requirements for market risk", [online], January 2016, Basel Committee on Banking Supervision, [searched July 11, 2016], Internet <URL: http://www.bis.org /bcbs/publ/d352.pdf> “Overview of“ Minimum Market Risk Capital ”, [online], March 2016, Financial Services Agency / Bank of Japan, [July 11, 2016 search], Internet <URL: http: // www .boj.or.jp / announcements / release_2016 / data / rel160118b1.pdf>

  In the FRTB capital charge calculation method, the standard method is to calculate the capital charge based on the sensitivity to the fluctuation factors (risk factors) of the position held. The calculation method is defined in detail by the Basel Committee on Banking Supervision. It has been. On the other hand, the internal model method is a method in which each financial institution calculates the capital charge based on its own model based on the guidelines of the Basel Committee on Banking Supervision. However, each trading desk requires approval from the authorities for the model. Therefore, financial institutions are thought to have a need to calculate capital charges based on standard methods at low cost in order to report to the authorities appropriately and at a low cost.

  On the other hand, the calculation of the capital charge is performed by summing up those calculated for each trading transaction, but the number of transactions increases to thousands to hundreds of thousands depending on the scale of the financial institution. At this time, if the capital charge is simply calculated for reporting to the authorities, it can be performed by nightly batch processing. However, for internal management of financial institutions, for example, there is a need to use simulation for portfolio optimization by grasping how much the capital charge will change when a specific transaction in the portfolio held is excluded. It is thought that there is also. In this case, for example, in a method in which the total capital charge is recalculated in a state where the target transaction is excluded and the difference from the capital charge before the exclusion is calculated, the calculation load increases, and the user satisfies the condition during the day. It is difficult to calculate the change each time while changing.

  Therefore, an object of the present invention is to calculate the capital charge by a standard method in FRTB and to efficiently grasp the fluctuation of the capital charge when one or more specific transactions are excluded from the holding portfolio. To provide a capital charge calculation system and a capital charge calculation method.

  The above and other objects and novel features of the present invention will be apparent from the description of this specification and the accompanying drawings.

  Of the inventions disclosed in this application, the outline of typical ones will be briefly described as follows.

  A capital charge calculation system according to a typical embodiment of the present invention is a capital charge calculation system for calculating a capital charge of a financial institution's trading account according to a standard method in FRTB, and is for each trading transaction in a holding portfolio. Calculating a calculation element including sensitivity to each risk factor in accordance with the regulatory requirements in the standard method, and recording the sensitivity calculation unit in the sensitivity recording unit, and the calculation element recorded in the sensitivity recording unit Based on the regulatory requirements, calculate a first capital charge for the holding portfolio and record it in the capital charge recording part; and for the one or more specified exclusion transactions, From the first capital charge for the second capital charge when excluded from the holding portfolio The dynamic component is calculated, having a capital charge variation analysis unit for recording the fluctuation analysis result recording unit.

  Then, the capital charge fluctuation analysis unit calculates the calculation element necessary for calculating the second capital charge in accordance with the regulatory requirements from the calculation element recorded in the sensitivity recording unit. It is acquired by removing the part concerning.

  Among the inventions disclosed in the present application, effects obtained by typical ones will be briefly described as follows.

  That is, according to the representative embodiment of the present invention, the capital charge is calculated by the standard method in the FRTB, and the fluctuation of the capital charge when one or more specific transactions are excluded from the holding portfolio is efficiently calculated. It becomes possible to grasp it.

It is the figure which showed the outline | summary about the structural example of the capital imposition calculation system which is one embodiment of this invention. It is the figure which showed the outline | summary about the example of a screen which displays the analysis result of the fluctuation part of capital charge in one embodiment of this invention. It is the figure which showed the outline | summary about the other example of a screen which displays the analysis result of the fluctuation part of the capital charge in one embodiment of this invention. It is the flowchart which showed the outline | summary about the example of the flow of a process which calculates the fluctuation | variation part of the capital charge in one embodiment of this invention. It is the table | surface which showed the combination of the risk class and risk type used as the total unit of capital charge in one embodiment of this invention. It is the flowchart which showed the outline | summary about the example of the flow of a process which calculates the capital charge in a standard system. It is the flowchart which showed the outline | summary about the example of the flow of a process which calculates the fluctuation | variation part of capital charge when the method assumed as a general thing is taken.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Note that components having the same function are denoted by the same reference symbols throughout the drawings for describing the embodiment, and the repetitive description thereof will be omitted. On the other hand, parts described with reference numerals in some drawings may be referred to with the same reference numerals although not illustrated again in the description of other drawings.

<System configuration>
FIG. 1 is a diagram showing an outline of a configuration example of a capital charge calculation system according to an embodiment of the present invention. The capital charge calculation system 1 is an information processing system having a function of calculating and outputting a capital charge by a standard method in FRTB based on information on trading transactions in a financial institution. Then, when calculating the total capital charge, the predetermined intermediate calculation result is retained and used to calculate the amount of change in the capital charge when one or more specific transactions are excluded from the holding portfolio. , It has a function of efficiently calculating without re-calculating the whole.

  The capital charge calculation system 1 includes, for example, a server device, a virtual server built on a cloud computing environment, or an information processing apparatus such as a PC (Personal Computer). A CPU (Central Processing Unit) executes middleware such as an OS (Operating System), a DBMS (DataBase Management System), a Web server program, and the like that are expanded on a memory (not shown), and various software running on the middleware. Thus, various functions to be described later are realized. At that time, various data stores held on a recording medium such as a hard disk device (not shown) are referred to / updated.

  The capital charge calculation system 1 includes components such as an input unit 11, sensitivity calculation unit 12, capital charge calculation unit 13, capital charge fluctuation analysis unit 14, and user interface unit 15 that are implemented as software that operates on the above middleware. Have Also, setting information 31 implemented as a file table, risk factor (RF) setting information 41 that holds reference data such as an aggregation key and parameters for calculating capital charges, risk weight (RW) setting information 42, Each data store includes bucket setting information 43 and correlation setting information 44. In addition, each data store such as a transaction information database (DB) 21 implemented as a database, a sensitivity database (DB) 51 holding a result relating to the calculation of capital charge, a capital charge DB 52, and a fluctuation analysis result DB 53 is stored. Have.

  The input unit 11 has a function of a data input interface for acquiring input data such as transaction data necessary for calculating capital charges from the outside. The input data includes, for example, data such as transaction market information and calendar information in addition to transaction data related to a trading account. Further, various setting information such as output item settings may be included. The input data is recorded in, for example, the transaction information DB 21 or the setting information 31. In that case, you may perform the process converted into the data format which the capital charge calculation system 1 can process. These input data can be acquired from, for example, an accounting system that performs trading transactions of a target financial institution, an information system that acquires and holds transaction data, a data source 2 such as a database server or a data warehouse. .

  The sensitivity calculation unit 12 has a function of calculating factors such as sensitivity to each risk factor, which is necessary when calculating capital charges by the FRTB standard method. For example, based on the transaction data recorded in the transaction information DB 21 and various reference data such as RF setting information 41, RW setting information 42, bucket setting information 43, and correlation setting information 44, the method described later The sensitivity for each risk factor is calculated every time and recorded in the sensitivity DB 51. In various reference data of the RF setting information 41, the RW setting information 42, the bucket setting information 43, and the correlation setting information 44, an aggregation key, a parameter, and the like used in a capital charge calculation model according to a standard method are set. All or some of the calculation functions of the sensitivity calculation unit 12 may be included in other external systems. In this case, the result calculated by another system or the like is acquired via the input unit 11.

  The capital charge calculation unit 13 has a function of calculating the capital charge of the trading account of the target financial institution by the FRTB standard method. For example, based on data such as sensitivity for each risk factor recorded in the sensitivity DB 51 and various reference data such as RF setting information 41, RW setting information 42, bucket setting information 43, and correlation setting information 44, which will be described later. By such a method, the capital charge is calculated for each transaction and recorded in the capital charge DB 52. The calculated capital charge data can be referred to for risk management by a user such as a person in charge of a financial institution via a user interface unit 15 described later, and also for reporting to the authorities. Can be used.

  The capital charge fluctuation analysis unit 14 has a function of calculating the fluctuation of the capital charge when a specific transaction or transaction set is excluded from the capital charge information of the trading account recorded in the capital charge DB 52. For example, the designation of a transaction or transaction set to be excluded is accepted based on an instruction from the user via the user interface unit 15 described later. Then, based on various reference data such as RF setting information 41, RW setting information 42, bucket setting information 43, and correlation setting information 44, a change in capital charge when a target transaction is excluded by a method described later. Calculate the minutes. The calculation result is recorded in the fluctuation analysis result DB 53.

  The user interface unit 15 has a function of providing an input / output interface with a screen to a web browser (not shown) on the user terminal 3 used by a user such as a person in charge of a financial institution by a web server program (not shown). For example, an input of a reference request for a calculation result of capital charge from a user is received, and the calculation results are aggregated and processed and output on the user terminal 3. In addition, it accepts the designation of transactions and transaction sets to be excluded from the user, calculates and extracts the capital charge fluctuation, processes the calculation result, and outputs it on the user terminal 3 through a screen as described later.

<Screen example>
FIG. 2 is a diagram showing an outline of a screen example that displays an analysis result of a change in capital charge displayed on the user terminal 3 by the user interface unit 15. In the example of FIG. 2, the capital charge of the trading account in the target financial institution is shown in a state in which it is possible to grasp the fluctuation amount of the capital charge when excluded in individual transaction units. Specifically, for each trading desk that has jurisdiction, a transaction No. The transaction name is displayed for each individual transaction specified in. Furthermore, the fluctuation amount of the capital charge for each risk class / risk type when the target transaction is excluded, and the fluctuation amount obtained by subtracting this from the transaction unit are displayed. As a result, transaction No. It is possible to grasp the amount of change in the capital charge when the specific transaction specified in (1) is excluded from the holding portfolio. Details of the risk class and risk type will be described later.

  FIG. 3 is a diagram showing an overview of another screen example that displays the analysis result of the change in capital charge displayed on the user terminal 3 by the user interface unit 15. In the example of FIG. 3, the fluctuation of the capital charge when the capital charge of the trading account in the target financial institution is excluded in units of transaction sets including a plurality of transactions is shown. Specifically, for the transaction set to be excluded specified by the user (“Set 001” in the example in the figure), the amount of change in capital charge and the subtotal by risk type are displayed for each risk class. Yes. Thereby, it is possible to grasp the fluctuation amount of the capital charge when the transaction set designated as the excluded transaction set is excluded from the holding portfolio.

  In the examples of FIGS. 2 and 3, the fluctuation of the capital charge is calculated in advance for every transaction or transaction set, for example, by night batch processing, and the corresponding calculation result in accordance with the instruction from the user. You may make it display. Or, instead of calculating in advance, for the specific transaction or transaction set specified by the user, calculate the amount of change in the capital charge when this is excluded, and display the calculation result Also good. Further, as shown in the example of FIG. 3, the transaction set may be selected from preset ones, or the user may select from the transaction list each time.

<Process flow>
FIG. 7 shows the amount of change in capital charge when the method assumed as a general one (hereinafter sometimes referred to as “general method”) is used instead of the method in the present embodiment. It is the flowchart which showed the outline | summary about the example of the flow of a process to perform. First, a capital charge for the entire owned portfolio, which is the basis for calculating the fluctuation of the capital charge, is calculated (S101).

  The capital charge is calculated based on the sensitivity required for each variable factor (risk factor) in each transaction. Sensitivity is an index representing price fluctuations with respect to fluctuations in risk factors. Each risk factor belongs to any one of 11 risk classes corresponding to the asset class and three risk types depending on the type of risk. FIG. 5 is a table showing combinations of risk classes and risk types as a unit for calculating capital charges. Each row of the table shows 11 risk classes, and the three columns on the right side of the table show three risk types, respectively.

  Risk classes include general interest rate risk (GIRR), non-securitized products, securitized products (non-CTP) and securitized products (CTP) credit spread risk (CSR), equity risk (equity), commodity risk ( Includes: Commodity, Foreign Exchange Risk, Securitized Products, Securitized Products (Non-CTP) and Securitized Products (CTP) Default Risk (Default), and Residual Risk Add-on . Of these, for general interest rate risk, credit spread risk, equity risk, commodity risk, and foreign exchange risk, capital charges are calculated based on the sensitivity of each risk type.

  Risk types consist of delta and vega risk linear risks and non-linear risks. Delta risk is the sensitivity to changes in the underlying asset price. Vega risk is the sensitivity to changes in the underlying asset price volatility (implied volatility). Non-linear risk is a risk exposure for the part of the risk that cannot be captured by linear risk when the underlying asset price fluctuates significantly.

  As described above, each risk factor belongs to one of a combination of a risk class and a risk type (“◯” in the figure). Since one product may have a plurality of risk factors, the sensitivity may be calculated in a plurality of risk classes even for one product. As shown below, for each transaction, the amount of capital charge for each risk class and risk type is calculated, and the final capital charge is calculated by simply summing them.

  FIG. 6 is a flowchart showing an outline of an example of the flow of processing for calculating the capital charge. The processing content here is in accordance with the calculation method of capital charge by the standard method in FRTB shown in Non-Patent Documents 1-3.

  First, delta risk, vega risk, and non-linear risk are calculated (S10). Specifically, first, the sensitivity for each transaction and each risk factor is calculated based on the transaction data (S11). Then, the weighted sensitivity is calculated by multiplying the obtained sensitivity by a predetermined risk weight value (S12). Thereafter, the obtained weighted sensitivity data is tabulated for each bucket (classification) based on the correlation between risk factors defined in the regulatory requirements in FRTB (S13). Then, the tabulation results for each bucket are tabulated for each risk class and each risk type based on the correlation between buckets defined in the FRTB regulatory requirements (S14).

  Next, a default risk is calculated (S20). Specifically, first, a default risk value is calculated based on the transaction data (S21). Here, the value of JTD (Jump To Default) in gross is calculated based on the regulatory requirements in FRTB. Then, a position that can be offset by selling and buying is specified, and the value of the default risk that has been offset is calculated (S22). Here, the JTD value on the net is calculated based on the regulatory requirements in FRTB. Thereafter, the net JTD values obtained are tabulated for each bucket, taking into account the risk weights defined in the FRTB regulatory requirements and the unbalanced sales ratio (S23). Then, the aggregation results for each bucket are aggregated for each risk class based on the correlation between buckets defined in the regulatory requirements in FRTB (S24).

  Next, a residual risk is calculated (S30). In this case, based on the transaction data, the transactions for which the residual risk is calculated are aggregated by multiplying the assumed principal by the risk weight. Finally, the final capital charge is calculated by simply adding the calculation results in steps S10, S20, and S30 (S40). Through the above series of processes, the overall final capital charge can be calculated.

  Returning to FIG. 7, thereafter, the amount of change in the capital charge when a specific transaction or transaction set is excluded is calculated individually. First, a specific transaction (or transaction set) is virtually excluded from the portfolio (S103). Thereafter, with the transaction excluded, the capital charge is recalculated by the same method as in step S101 (S104). Then, by subtracting the capital charge recalculated in step S104 from the capital charge calculated in step S101, the difference is calculated, thereby calculating the fluctuation of the capital charge when the target transaction (or transaction set) is excluded. (S105).

  Thereafter, it is determined whether or not there are transactions (or transaction sets) to be excluded (S106). If there is (S106: Yes), the process returns to step S103, and a series of processing is repeated until there are no transactions (or transaction sets) to be excluded in step S106. If there is no transaction (or transaction set) to be excluded (S106: No), the calculation results so far are output (S107), and the process is terminated.

  When calculating the fluctuation of the capital charge according to the example of FIG. 7, the processing load for recalculating the capital charge in step S104 is high. Therefore, if this process is repeated for the number of transactions (or transaction sets) to be excluded, the processing time It will take too much. Therefore, in the present embodiment, as described above, the intermediate calculation result obtained when the total capital charge is calculated in step S101 is stored and used to calculate the fluctuation amount of the capital charge. In addition, it is unnecessary to recalculate the total capital charge.

  FIG. 4 is a flowchart showing an outline of an example of a flow of processing for calculating the fluctuation amount of the capital charge by the capital charge calculation system 1. First, the capital charge of the entire holding portfolio, which is the basis for calculating the fluctuation of the capital charge, is calculated (S01). Since the processing contents are the same as those in step S101 in the example of FIG. Next, a predetermined one of the intermediate calculation results calculated when the total capital charge is calculated in step S01 is recorded in the sensitivity DB 51 or the like (S02). Here, for convenience, it is described as a step independent of step S01, but may be recorded as appropriate during the calculation process of step S01.

  Then, the amount of change in capital charge when a specific transaction or transaction set is excluded is calculated individually. First, a specific transaction (or transaction set) is excluded from the portfolio (S03). In this state, the capital charge for the entire portfolio is calculated. At that time, unlike the recalculation of the entire transaction in step S104 in the example of FIG. 7, the intermediate calculation result recorded in step S02 is used to recalculate only the portion affected by the excluded transaction (or transaction set). The calculation is performed by limiting the range of (S04). A specific calculation method using the intermediate calculation result will be described later. Further, since the subsequent processing contents (steps S05 to S07) are the same as steps S105 to S107 in the example of FIG.

<Calculation method>
In the following, the specific contents of the calculation method for the change in capital charge in the present embodiment shown in FIG. 4 will be described in comparison with the general method for calculating the change in capital charge shown in FIG. . As described above, both the method of the present embodiment and the general method basically calculate the capital charge of the entire portfolio by the method shown in FIG. 6 (step S01 in FIG. 7 (step S101), and thereafter, a capital charge in a state where a specific transaction (or transaction set) is excluded is calculated (step S04 in FIG. 4 and step S104 in FIG. 7). Then, the fluctuation amount of the capital charge is calculated from these differences (step S05 in FIG. 4 and step S105 in FIG. 7).

≪Linear risk (Delta risk, Vega risk) ≫
In calculating the total capital charge, for the delta risk / vega risk that is a linear risk, first, the sensitivity calculation unit 12 calculates the weighted sensitivity for each risk factor (steps S11 and S12 in FIG. 6). The weighted sensitivity WS _k for the risk factor k for the transaction set (1, 2,..., I,..., I) recorded in the transaction information DB 21 is expressed by the following equation.

Here, RW _k is a risk weight for each risk factor k preset in the RW setting information 42 (the same applies to the following formulas). The contents of each risk factor are preset in the RF setting information 41. The weighted sensitivity WS _k calculated by the equation 1 is recorded in the sensitivity DB 51.

Next, the sensitivity calculation unit 12 totals the weighted sensitivity for each risk factor for each bucket (step S13 in FIG. 6). Bucket risk K _b for risk factor set X (1, 2,..., K,..., R) belonging to bucket _b is expressed by the following expression.

Here, ρ _kl is a correlation coefficient between the risk factor k and the risk factor l set in advance in the correlation setting information 44 (the same applies to the following equations). The contents of each bucket are set in the bucket setting information 43 in advance. The bucket risk K _b calculated by Equation 2 is also recorded in the sensitivity DB 51.

Next, the capital charge calculation unit 13 collects the bucket risk for each bucket for each risk class and each risk type to obtain a capital charge (step S14 in FIG. 6). Delta risk and Vega risk as capital charges are respectively expressed by the following formulas.

Here, γ _bc is a correlation coefficient between buckets b and c preset in the correlation setting information 44 (the same applies to the following equations). The capital charge (delta risk, vega risk) calculated by Equation 3 is recorded in the capital charge DB 52.

Thereafter, the capital charge fluctuation analysis unit 14 calculates the capital charge in a state where a specific transaction (or transaction set) is excluded. Here, in the general method (step S104 in FIG. 7), the calculation according to the above formulas 1 to 3 is performed again after excluding specific transactions. On the other hand, in the present embodiment (step S04 in FIG. 4), the weighted sensitivity WS _k calculated by Equation 1 and Equation 2 for the transaction set including all transactions and recorded in the sensitivity DB 51. And the intermediate calculation result of the bucket risk K _b is used to simplify the calculation.

Specifically, the weighted sensitivity WS _k ′ for the risk factor k after excluding the excluded transaction set (1, 2,..., I,..., I ′) from all transactions is expressed by the following equation. .

Here, WS _{k in} the first term on the right side is the weighted sensitivity as an intermediate calculation result that is already calculated by Equation 1 and recorded in the sensitivity DB 51 when calculating the capital charge for all transactions. It is. In the second term on the right side, the number of additions is limited to I ′ (number of transactions to be excluded) compared to Equation 1, and the number is very small. Therefore, the calculation load is greatly reduced as compared with the general method.

Further, after excluding the excluded transaction set (1, 2,..., I,..., I ′) from all the transactions, the risk factor set X (1, 2,..., K belonging to the bucket b affected by the transaction exclusion. ,..., R ′), the bucket risk K _b ′ is expressed by the following equation.

Here, _Kb of the first term in the right-hand side square root is calculated as an intermediate calculation result that is already calculated by Equation 2 and recorded in the sensitivity DB 51 when calculating the capital charge for all transactions. Bucket risk. Then, the parenthesis, which is the second term in the square root on the right side, is a term for excluding an element affected by the risk factor set X belonging to the bucket b that is affected by the transaction exclusion, as compared with the equation (2). . The parenthesis, which is the third term in the square root on the right side, is a term for replacing the above-excluded element with a recalculated considering the effect of transaction exclusion. Also for these terms, the number of additions is limited to R ′ (the number of risk factors included in the bucket b affected by the transaction exclusion) and is a small number compared to the equation (2). Therefore, the calculation load is reduced as compared with the general method.

  In addition, since the original calculation amount is small in the calculation for collecting the bucket risk for each risk class and each risk type to obtain the capital charge, Equation 3 is used without any special consideration. With the above processing, it is possible to reduce the load required for calculating the capital charge (delta risk, vega risk) in a state where a specific transaction (or transaction set) is excluded. Subsequent processing for calculating the amount of change in capital charge is the same for both the method of the present embodiment (steps S05 to S07 in FIG. 4) and the general method (steps S105 to S107 in FIG. 7).

≪Nonlinear risk≫
For the nonlinear risk, first, the sensitivity calculation unit 12 calculates the nonlinear risk for each risk factor (steps S11 and S12 in FIG. 6). The non-linear risk CVR _k for the risk factor k for the calculation target transaction set (1, 2,..., I,..., I) recorded in the transaction information DB 21 is expressed by the following equation.

Here, V _i is the market price of the transaction i at the level of the risk factor k related to the transaction i. Further, V _ik ⁺ and V _ik ⁻ are the market prices of the transaction i when the risk weight of delta risk is added to or subtracted from the level of the risk factor k related to the transaction i (the same applies to the following equations). The nonlinear risk CVR _k calculated by the equation 6 is recorded in the sensitivity DB 51.

Next, the non-linear risk for each risk factor is tabulated for each bucket by the sensitivity calculation unit 12 (step S13 in FIG. 6). Bucket risk K _b for risk factor set X (1, 2,..., K,..., R) belonging to bucket _b is expressed by the following expression.

The bucket risk K _b calculated by Equation 7 is also recorded in the sensitivity DB 51.

Next, the capital charge calculation unit 13 collects the bucket risk for each bucket for each risk class and each risk type to obtain a capital charge (step S14 in FIG. 6). Non-linear risk as capital charge is expressed by the following formula.

  The capital charge (non-linear risk) calculated by Equation 8 is recorded in the capital charge DB 52.

Thereafter, the capital charge fluctuation analysis unit 14 calculates the capital charge in a state where a specific transaction (or transaction set) is excluded. Here, in the general method (step S104 in FIG. 7), the calculation according to the above formulas 6 to 8 is performed again after excluding a specific transaction. On the other hand, in the present embodiment (step S04 in FIG. 4), the nonlinear risk CVR _k calculated by Equation 6 and Equation 7 for the transaction set including all transactions and recorded in the sensitivity DB 51 and The calculation is simplified using the intermediate calculation result of the bucket risk K _b .

Specifically, the non-linear risk CVR _k ′ for the risk factor k after excluding the excluded transaction set (1, 2,..., I,..., I ′) from all transactions is expressed by the following expression.

Here, CVR _k ⁺ and CVR _k ⁻ of the first term of each element in the min function on the right side are already calculated by Equation 6 and recorded in the sensitivity DB 51 when calculating the capital charge for all transactions. It is a non-linear risk as an intermediate calculation result. In addition, in the parentheses, which is the second term of each element, the number of additions is limited to I ′ (number of transactions to be excluded), which is a very small number, as compared with Equation 6. Therefore, the calculation load is greatly reduced as compared with the general method.

Further, after excluding the excluded transaction set (1, 2,..., I,..., I ′) from all the transactions, the risk factor set X (1, 2,..., K belonging to the bucket b affected by the transaction exclusion. ,..., R ′), the bucket risk K _b ′ is expressed by the following equation.

Here, K _{b, pre} of the first term of the non-zero element in the right-side max function is already calculated by Equation 7 and recorded in the sensitivity DB 51 when calculating the capital charge for all transactions. It is obtained from the bucket risk as an intermediate calculation result. The parentheses that are the second term of the non-zero element are the terms for excluding the elements that are affected by the risk factor set X belonging to the bucket b that is affected by the transaction exclusion, as compared with the equation (7). is there. Then, the parentheses that are the third term of the non-zero element are terms for replacing the excluded elements with those recalculated in consideration of the influence of transaction exclusion. Also for these terms, the number of additions is limited to R ′ (the number of risk factors included in the bucket b affected by transaction exclusion) as compared with the equation (7), which is a small number. Therefore, the calculation load is reduced as compared with the general method.

  Note that, as in the case of delta risk and vega risk described above, the subsequent calculations for calculating the bucket risk by risk class and risk type to obtain the capital charge should be considered especially because the original calculation amount is small. The equation 8 is used as it is. With the above processing, it is possible to reduce the load required for calculating the capital charge (nonlinear risk) in a state where a specific transaction (or transaction set) is excluded. Subsequent processing for calculating the amount of change in capital charge is the same for both the method of the present embodiment (steps S05 to S07 in FIG. 4) and the general method (steps S105 to S107 in FIG. 7).

≪Default risk (non-securitized products) ≫
For the default risk associated with non-securitized products, first, the sensitivity calculation unit 12 calculates gross JTD and net JTD (steps S21 and S22 in FIG. 6). Gross JTD (JTD _{k, s,} J) for issuer k, asset superiority / inferiority category s, and long / short category l for the transaction set (1, 2,..., I,..., I) recorded in the transaction information DB 21 _{. l} ) is expressed by the following equation.

The gross JTD _{k, s, l} calculated by Equation 11 is recorded in the sensitivity DB 51. Then, considering the asset superiority / inferiority relationship, net JTD _{k, l} is calculated by offsetting gross JTD for each netting set for the same asset superiority / inferiority category s.

Next, the sensitivity calculation unit 12 aggregates the net JTD for each issuer and each long / short section for each bucket (step S23 in FIG. 6). The capital charge DRC _b relating to the bucket b is expressed by the following equation.

The capital charge DRC _b calculated by Equation 12 is recorded in the sensitivity DB 51. Then, the capital charge calculation unit 13 simply sums the capital charges DRC _b for each bucket to obtain a capital charge for each risk class (step S24 in FIG. 6).

Thereafter, the capital charge fluctuation analysis unit 14 calculates the capital charge in a state where a specific transaction (or transaction set) is excluded. Again, in the general method (step S104 in FIG. 7), the calculation according to the above equations 11 to 12 is performed again after excluding specific transactions. On the other hand, in the present embodiment (step S04 in FIG. 4), the intermediate of gross JTD _{k, s, l} calculated by Equation 11 for the transaction set including all transactions and recorded in the sensitivity DB 51. Use the calculation result to simplify the calculation.

Specifically, gross JTD (JTD _k ) for issuer k, asset superiority / inferiority category s, and long / short category 1 after excluding the excluded transaction set (1, 2,..., I,..., I ′) from all transactions. _{, s, l} ′) is expressed by the following equation.

Here, JTD _{k, s, l in} the first term on the right-hand side is an intermediate calculation result that is already calculated by Equation 11 and recorded in the sensitivity DB 51 when calculating the capital charge for all transactions. Gross JTD. In the second term on the right side, the number of additions is limited to I ′ (the number of transactions to be excluded), which is a very small number, as compared with Equation (11). Therefore, the calculation load is greatly reduced as compared with the general method.

  In addition, since the calculation from net JTD calculation to totaling for each bucket and totaling for each risk class is not so high as the original calculation charge, it is difficult to obtain a large improvement effect. Thus, the same method as the general method is taken. With the above processing, it is possible to reduce the load required for calculating the capital charge (default risk relating to non-securitized products) in a state where a specific transaction (or transaction set) is excluded. Subsequent processing for calculating the amount of change in capital charge is the same for both the method of the present embodiment (steps S05 to S07 in FIG. 4) and the general method (steps S105 to S107 in FIG. 7).

≪Default risk (securitized products, non-CTP) ≫
For the default risk relating to securitized products (non-CTP), first, the sensitivity calculation unit 12 calculates gross JTD and net JTD (steps S21 and S22 in FIG. 6). Gross JTD (JTD _{k, l} ) for netting set k, asset superiority / inferiority category s, and long / short category 1 for the transaction set (1, 2,..., I,...) Recorded in the transaction information DB 21. Is represented by the following equation.

The gross JTD _{k, l} calculated by Equation 14 is recorded in the sensitivity DB 51. The subsequent calculation from net JTD calculation to aggregation for each bucket and aggregation for each risk class is the same as the calculation of the default risk of the non-securitized product, and the description thereof will be omitted.

Thereafter, the capital charge fluctuation analysis unit 14 calculates the capital charge in a state where a specific transaction (or transaction set) is excluded. Again, in the general method (step S104 in FIG. 7), the calculation based on the above-mentioned formulas 14 and 12 is performed again after excluding specific transactions. On the other hand, in the present embodiment (step S04 in FIG. 4), an intermediate calculation result of gross JTD _{k, l} , which is calculated by Equation 14 for the transaction set including all transactions and recorded in the sensitivity DB 51. To simplify the calculation.

Specifically, the gross JTD (JTD _k ) for the netting set k, the asset superiority / inferiority category s, and the long / short category 1 after excluding the excluded transaction set (1, 2,..., I,..., I ′) from all transactions. _{, l} ′) is expressed by the following equation.

Here, JTD _{k, l in} the first term on the right-hand side is the gross calculation result as an intermediate calculation result that is already calculated by Equation 14 and recorded in the sensitivity DB 51 when calculating the capital charge for all transactions. JTD. In the second term on the right side, the number of additions is limited to I ′ (the number of transactions to be excluded) compared to the equation (14), and the number is very small. Therefore, the calculation load is greatly reduced as compared with the general method.

  Since the subsequent calculation from net JTD calculation to aggregation for each bucket and aggregation for each risk class is the same as the calculation of default risk of the non-securitized product, the description thereof will be omitted. With the above processing, it is possible to reduce the load required for calculating the capital charge (default risk relating to securitized products (non-CTP)) in a state where a specific transaction (or transaction set) is excluded. Subsequent processing for calculating the amount of change in capital charge is the same for both the method of the present embodiment (steps S05 to S07 in FIG. 4) and the general method (steps S105 to S107 in FIG. 7).

≪Default risk (securitized products / CTP) ≫
For the default risk related to securitized products (CTP), first, the sensitivity calculation unit 12 calculates gross JTD and net JTD (steps S21 and S22 in FIG. 6). Gross JTD (JTD _{k, s,} J) for the netting set k, asset superiority / inferiority category s, and long / short category 1 for the transaction set (1, 2,..., I,. _l ) is expressed by the following equation similar to equation (14).

The gross JTD _{k, s, l} calculated by the equation 16 is recorded in the sensitivity DB 51. Then, considering the asset superiority / inferiority relationship, net JTD _{k, l} is calculated by offsetting gross JTD for each netting set for the same asset superiority / inferiority category s.

Next, the sensitivity calculation unit 12 aggregates the net JTD for each netting set and each long / short section for each bucket (step S23 in FIG. 6). The capital charge DRC _b relating to the bucket b is expressed by the following equation.

The capital charge DRC _b calculated by Equation 17 is recorded in the sensitivity DB 51.

Next, the capital charge calculation unit 13 calculates the capital charge DRC _b for each bucket for each risk class to obtain a capital charge (step S24 in FIG. 6). The default risk DRC _CTP as a capital charge is expressed by the following formula.

  The capital charge (default risk relating to securitized products (CTP)) calculated by Equation 18 is recorded in the capital charge DB 52.

Thereafter, the capital charge fluctuation analysis unit 14 calculates the capital charge in a state where a specific transaction (or transaction set) is excluded. Again, in the general method (step S104 in FIG. 7), the calculation according to the above equations 16 to 18 is performed again after excluding specific transactions. On the other hand, in the present embodiment (step S04 in FIG. 4), an intermediate calculation result of gross JTD _{k, l} calculated by Equation 16 for the transaction set including all transactions and recorded in the sensitivity DB 51. To simplify the calculation.

Specifically, the gross JTD (JTD _k ) for the netting set k, the asset superiority / inferiority category s, and the long / short category 1 after excluding the excluded transaction set (1, 2,..., I,..., I ′) from all transactions. _{, l} ′) is expressed by the following equation similar to equation (15).

Here, JTD _{k, l in} the first term on the right side is a gross calculation result as an intermediate calculation result that is already calculated by Equation 16 and recorded in the sensitivity DB 51 when calculating the capital charge for all transactions. JTD. In the second term on the right side, the number of additions is limited to I ′ (the number of transactions to be excluded) compared to the equation (16), and the number is very small. Therefore, the calculation load is greatly reduced as compared with the general method.

  In addition, since the calculation from net JTD calculation to totaling for each bucket and totaling for each risk class is not so high as the original calculation charge, it is difficult to obtain a large improvement effect. Thus, the same method as the general method is taken. With the above processing, it is possible to reduce the load required for calculating the capital charge (default risk relating to securitized products (CTP)) in a state where a specific transaction (or transaction set) is excluded. Subsequent processing for calculating the amount of change in capital charge is the same for both the method of the present embodiment (steps S05 to S07 in FIG. 4) and the general method (steps S105 to S107 in FIG. 7).

≪Residual risk≫
Thereafter, the residual risk is calculated by the capital charge calculation unit 13 (step S30 in FIG. 6). The residual risk X for the assumed principal s for the transaction set (1, 2,..., I,..., I) recorded in the transaction information DB 21 is expressed by the following equation.

  The residual risk X calculated by Equation 20 is recorded in the sensitivity DB 51.

  Thereafter, in the general method (step S104 in FIG. 7), in order to calculate the fluctuation of the capital charge when a specific transaction (or transaction set) is excluded, the capital charge in that state is calculated by the above equation (20). It will be calculated again. On the other hand, in the present embodiment, unlike the other risk types described above, the residual risk is calculated directly by calculating the amount of change in capital charge resulting from the exclusion of specific transactions by the capital charge fluctuation analysis unit 14. , Simplify the calculation.

Specifically, the fluctuation amount X ′ of the residual risk for the assumed principal s after excluding the excluded transaction set (1, 2,..., I,..., I ′) from all the transactions is directly calculated by the following equation. Can be calculated.

  Here, the number of additions is limited to I ′ (number of transactions to be excluded) compared to the equation (20), and the right side is a very small number. Therefore, the calculation load is greatly reduced as compared with the general method.

  As described above, according to the capital charge calculation system 1 which is an embodiment of the present invention, when calculating the capital charge of the entire transaction, the obtained weighted sensitivity, bucket risk, gross JTD, etc. The intermediate calculation result is recorded in the sensitivity DB 51. And in order to calculate the amount of change in the capital charge when a specific transaction (or transaction set) is excluded, an intermediate calculation recorded in the sensitivity DB 51 when calculating the capital charge with the transaction excluded Use the results to simplify the calculation. That is, intermediate calculation elements such as weighted sensitivity, bucket risk, and gross JTD that are required when calculating capital charges are recorded in the sensitivity DB 51 instead of being recalculated for the entire transaction after exclusion. Calculation is performed by removing the part related to the excluded transaction from the interim calculation result.

Examples of removal methods include those that subtract elements related to excluded transactions such as weighted sensitivity WS _k ′, and elements that are affected by excluded transactions such as bucket risk K _b ′. Some have been deleted and replaced with recalculated elements with transactions excluded. Others, such as residual risk, can directly calculate the amount of change in capital charges when transactions are excluded.

  By using this calculation method, the number of additions in the specified addition process when calculating capital charges (or fluctuations) when transactions are excluded is the number of transactions after exclusion in the general method. In the present embodiment, the number of excluded transactions can be set. As mentioned above, the trading transactions that are subject to calculation are as large as thousands to hundreds of thousands depending on the size of the financial institution, and even if a specific transaction set is excluded, Therefore, the number of excluded transactions is considered to be overwhelmingly small. Therefore, the calculation load can be greatly reduced by adopting the calculation method as in the present embodiment.

  As mentioned above, the invention made by the present inventor has been specifically described based on the embodiments. However, the present invention is not limited to the above-described embodiments, and various modifications can be made without departing from the scope of the invention. Needless to say. For example, the above-described embodiment has been described in detail for easy understanding of the present invention, and is not necessarily limited to the one having all the configurations described. In addition, it is possible to add, delete, and replace other configurations for a part of the configuration of the above-described embodiment.

  For example, in the above embodiment, the case where the fluctuation of the capital charge when a specific transaction (or transaction set) is excluded is calculated for the capital charge of the entire transaction is an example. The present invention can also be applied to the calculation of the amount of change when a transaction is added. In addition, when calculating the capital charge when a specific transaction is excluded, all the calculation elements (weighted sensitivity, bucket risk, etc.) required are all calculated as intermediate calculation results recorded in the sensitivity DB 51. It is not necessary to make the calculation more efficient by using it. It is only necessary that the calculation is made efficient by using the intermediate calculation results for at least some of the calculation elements that can be made efficient.

  Each of the above-described configurations, functions, processing units, processing means, and the like may be realized by hardware by designing a part or all of them with, for example, an integrated circuit. Each of the above-described configurations, functions, and the like may be realized by software by interpreting and executing a program that realizes each function by the processor. Information such as programs, tables, and files for realizing each function can be stored in a recording device such as a memory, a hard disk, or an SSD (Solid State Drive), or a recording medium such as an IC card, an SD card, or a DVD.

  Moreover, in each said figure, the control line and the information line have shown what is considered necessary for description, and do not necessarily show all the control lines and information lines on mounting. Actually, it may be considered that almost all the components are connected to each other.

  INDUSTRIAL APPLICABILITY The present invention can be used for a capital charge calculation system and a capital charge calculation method for calculating a capital charge for a market risk of a trading book based on capital regulations by the Basel Committee on Banking Supervision.

1 ... capital charge calculation system, 2 ... data source, 3 ... user terminal,
DESCRIPTION OF SYMBOLS 11 ... Input part, 12 ... Sensitivity calculation part, 13 ... Capital charge calculation part, 14 ... Capital charge fluctuation analysis part, 15 ... User interface part,
21 ... Transaction information DB,
31 ... setting information,
41 ... RF setting information, 42 ... RW setting information, 43 ... bucket setting information, 44 ... correlation setting information,
51 ... Sensitivity DB, 52 ... Capital charge DB, 53 ... Fluctuation analysis result DB

Claims (6)

A capital charge calculation system that calculates the capital charge for a financial institution's trading account using the standard method of the Fundamental Review of the Trading Book (FRTB) by the Basel Committee on Banking Supervision There,
A sensitivity calculation unit that calculates a calculation element including sensitivity to each risk factor in accordance with the regulatory requirements in the standard method for each trading transaction in the holding portfolio, and records it in the sensitivity recording unit;
Based on the calculation element recorded in the sensitivity recording unit, a capital charge calculating unit that calculates a first capital charge for the owned portfolio according to the regulatory requirements and records the capital charge in the capital charge recording unit;
For one or more specified exclusion transactions, the variation from the first capital charge is calculated for the second capital charge when the exclusion transaction is excluded from the holding portfolio, and the fluctuation analysis result A capital charge fluctuation analysis unit for recording in the recording unit;
The capital charge fluctuation analysis unit relates the calculation element necessary for calculating the second capital charge according to the regulatory requirements from the calculation element recorded in the sensitivity recording unit to the exclusion transaction. A capital charge calculation system that is obtained by removing parts. In the capital charge calculation system according to claim 1,
The capital charge fluctuation analysis unit deletes an element affected by the exclusion transaction when removing a portion related to the exclusion transaction from the calculation element recorded in the sensitivity recording unit, and removes the exclusion transaction. A capital charge calculation system that replaces elements that are recalculated in the excluded state. In the capital charge calculation system according to claim 1 or 2,
The calculation element acquired from the sensitivity recording unit when the capital charge fluctuation analysis unit calculates the second capital charge is a risk factor when calculating the fluctuation of the capital charge related to linear risk. A capital charge calculation system that is a weighted sensitivity and / or bucket risk. In the capital charge calculation system according to claim 1 or 2,
The calculation element acquired from the sensitivity recording unit when the capital charge fluctuation analysis unit calculates the second capital charge is a risk factor when calculating the fluctuation of the capital charge related to nonlinear risk. A capital charge calculation system that is non-linear risk and / or bucket risk. In the capital charge calculation system according to claim 1 or 2,
When the capital charge fluctuation analysis unit calculates the second capital charge, the calculation element acquired from the sensitivity recording unit is a gross JTD when calculating the fluctuation of the capital charge related to the default risk. The capital charge calculation system that is (Jump To Default). In the capital charge calculation system that calculates the capital charge of the trading account of a financial institution by the standard method in the “Fundamental Review of the Trading Book (FRTB)” by the Basel Committee on Banking Supervision A capital charge calculation method,
With the capital charge calculation system,
For each trading transaction in the holding portfolio, a first step of calculating a calculation element including sensitivity to each risk factor in accordance with the regulatory requirements in the standard method and recording it in the sensitivity recording unit;
A second step of calculating a first capital charge for the owned portfolio according to the regulatory requirements based on the calculation element recorded in the sensitivity recording section and recording it in a capital charge recording section;
For one or more specified exclusion transactions, the variation from the first capital charge is calculated for the second capital charge when the exclusion transaction is excluded from the holding portfolio, and the fluctuation analysis result A third step of recording in the recording unit,
In the third step, the calculation element necessary for calculating the second capital charge in accordance with the regulatory requirements is changed from the calculation element recorded in the sensitivity recording unit to a portion related to the exclusion transaction. Capital charge calculation method obtained by removing.

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