JP6875200B2 - Risk assessment system, risk assessment method and risk assessment program - Google Patents

Description

The present invention relates to a risk assessment system, a risk assessment method and a risk assessment program for assessing interest rate risk.

Fluctuations in interest rates affect bond prices. Therefore, a technique for evaluating interest rate risk is also being studied for bonds (credits) whose cash flow changes in response to interest rate fluctuations (see, for example, Patent Document 1). The interest rate risk assessment program described in this document calculates the cash flow of a bond using a mathematical model that represents the path of interest rate fluctuations over time, and uses that cash flow to calculate the effective duration of the bond.

Bayesian inference may also be used to predict the future. In this Bayesian estimation, based on the concept of Bayesian probability, the matter to be estimated (causal event that is the cause of it) is inferred in a probabilistic sense from the observed event (observed fact). A method for calculating a bankruptcy probability that can calculate a realistic probability regardless of the bankruptcy / non-bankruptcy ratio in the training data has also been studied (see, for example, Patent Document 2). In the techniques described in this document, the financial data of multiple companies is input, a decision tree is created from the financial data, the financial data of the target company is applied to the decision tree, Bayes' theorem is used, and the target company is used. Is applied to the decision tree to calculate the probability of default. Furthermore, a hierarchical Bayesian model that describes the relationship between parameters by the hierarchy of prior distribution-super prior distribution is also being studied.

Japanese Unexamined Patent Publication No. 2016-162417 Japanese Unexamined Patent Publication No. 2000-259719

In April 2016, the Basel Committee on Banking Supervision published the "Standards Interest rate risk in the banking book (IRRB)". Each financial institution is planning to support this IRRBB. IRRBB reviews the treatment of interest rate risk related to bank accounts by bank supervision (principles for management and supervision of interest rate risk), and requires stricter interest rate risk management.

Estimates for fixed interest rate loans with prepayment risk, fixed interest rate loan commitments, time deposits with early cancellation risk, and non-maturity deposits (NMDs) for interest rate risk management at each financial institution that needs to be dealt with It is necessary to consider the model.
Businesses at banks are classified into bank accounts that account for transactions centered on loans and deposits, and trading accounts that account for transactions that are conducted for the purpose of securing short-term trading margins due to fluctuations in interest rates. The bank account includes loans, deposits, and government bonds for the purpose of holding maturity, and the trading account includes receivables for the purpose of earning profits from daily trading. For interest rate risk in trading accounts, it was necessary to accumulate a certain amount of equity capital. Furthermore, it became necessary to strengthen the supervisory function for government bonds held in bank accounts.
Interest rate risk in a bank account is a risk caused by fluctuations in the market price or income of assets and liabilities in a bank account due to fluctuations in interest rate levels. Bank accounts are basically operated for the purpose of long-term holding of assets, etc., and in terms of regulation, the risk of bad debt (= credit risk) rather than the change in market price (= interest rate risk) due to fluctuations in interest rates, etc. Has been emphasized.

However, evaluation of factors related to behavioral options requires a large amount of data considering various situations, which is difficult to evaluate.
In addition, in order to create a statistical model that can be used by any number of financial institutions, it is convenient to have a mechanism that enables rational estimation without knowing the data structure. In addition, it is not realistic to obtain contract information from financial institutions in advance and create a statistical model dedicated to each financial institution each time. That is, it is difficult to secure the estimation accuracy when unknown data is input by the statistical model constructed from the static data of a specific financial institution.

The risk assessment system that solves the above problems is a public information storage unit that stores publicly available national information, an individual information storage unit that stores individual summary information that represents indicators in a specific institution, and a control unit that calculates risk indicators. And. Then, the control unit generates an interest rate prediction model and an index prediction model composed of a chain graphical model having a hierarchical Bayes structure in order to calculate the interest rate and the institution index using the published national information, and the specific institution. When the individual summary information for calculating the institutional index is obtained from, the index prediction model is adjusted by using the individual summary information, and the adjusted index is adjusted according to the interest rate calculated based on the interest rate prediction model. The institutional index prediction value is calculated using the prediction model, and the index prediction model is updated by Bayes using the newly released national information or the newly acquired individual summary information.

The present invention has been made to solve the above problems, and interest rate risk in any institution can be evaluated efficiently.

Explanatory drawing of the risk assessment system of this embodiment. The explanatory view of the processing procedure of this embodiment. Explanatory drawing of information used in this embodiment. The explanatory view of the processing procedure of this embodiment. The explanatory view of the processing procedure of this embodiment. The explanatory view of the processing procedure of this embodiment. The explanatory view of the processing procedure of this embodiment. The explanatory view of the processing procedure of this embodiment. The explanatory view of the processing procedure of this embodiment. The explanatory view of the processing procedure of this embodiment.

Hereinafter, an embodiment of a risk assessment system embodying the present invention will be described with reference to FIGS. 1 to 10. In this embodiment, it is assumed that IRRBB is evaluated using a hierarchical Bayesian model. Here, a chain graphical model (for example, a Bayesian network) is used as a hierarchical Bayesian model (Bayesian statistical model). This chain graphical model consists of two types of models, called a "system model" that expresses time-series fluctuations in data and an "observation model" that calculates target information (latent variables) from data at a certain point in time. It is composed. In this embodiment, this model is constructed by Bayesian statistics.

As shown in FIG. 1, in this embodiment, the client terminal 10 and the support server 20 are used.
The client terminal 10 is a computer terminal used by a user who uses this service. The client terminal 10 includes a control unit, an output unit, and an input unit. The control unit executes various applications. In the present embodiment, the control unit functions as a browser for accessing the support server 20. The output unit is composed of a display and outputs various information. The input unit is composed of a keyboard and a pointing device, and acquires an instruction input by the user.

The support server 20 is a computer system that evaluates interest rate risk using a hierarchical Bayesian model. The support server 20 includes a control unit 21, a public information storage unit 22, and an individual information storage unit 23.
The control unit 21 includes control means (CPU, RAM, ROM, etc.) and is described later in the processing (interest rate prediction stage, core deposit prediction stage, time deposit prediction stage, prepayment rate prediction stage, risk calculation stage, hedge simulation stage). Each process) is performed. By executing the risk assessment program for this purpose, the control unit 21 has the interest rate forecasting unit 211, the core deposit forecasting unit 212, the time deposit forecasting unit 213, the prepayment rate forecasting unit 214, the risk calculation unit 215, and the hedge simulation unit 216. Functions as.
The interest rate forecasting unit 211 predicts the future of the zero coupon yield curve and executes a process of calculating the discount rate.
The core deposit forecasting unit 212 executes a process of calculating the core deposit balance in the shock scenario using the hierarchical Bayesian model.
The time deposit prediction unit 213 executes a process of calculating the time deposit amount (balance) in the shock scenario using the hierarchical Bayes model.
The prepayment rate prediction unit 214 uses the hierarchical Bayesian model to execute a process of calculating the prepayment rate in the shock scenario.

The hierarchical Bayesian model used by the core deposit forecasting unit 212 to the prepayment rate forecasting unit 214 is generated using individual information and public information. When new individual information and public information are acquired, the hierarchical Bayesian model is updated.
The risk calculation unit 215 executes a process of calculating interest rate risk using the estimated interest rate, core deposit, fixed deposit amount, and prepayment rate.
The hedge simulation unit 216 executes a hedge simulation process corresponding to interest rate risk.

Comprehensive public information (here, national information) is recorded in the public information storage unit 22. The public information is recorded when the public information is acquired. This public information records the information needed to generate a hierarchical Bayesian model for calculating interest rates, core deposits, time deposits, and prepayment rates.
Individual information in a financial institution is recorded in the individual information storage unit 23. Individual information is recorded when individual information is obtained from a financial institution. In this individual information, information (individual summary information) for adjusting the hierarchical Bayesian model generated by using the public information is recorded.

(Outline of processing procedure)
The outline of the processing procedure will be described with reference to FIG. Here, a hierarchical Bayesian model is created with comprehensive information and IRRBB is predicted based on partial information.
First, the control unit 21 of the support server 20 executes a model creation process assuming every situation (step S1-1). Here, the published general information (national information) is used.

Next, the control unit 21 of the support server 20 executes the model adjustment process using the individual information (step S1-2). Here, individual information of a specific financial institution that conducts risk assessment is used.
Next, the control unit 21 of the support server 20 executes the prediction process based on the adjusted model (step S1-3). Here, the interest rate, core deposit, fixed deposit amount, and prepayment rate are calculated using a hierarchical Bayesian model.
Next, the control unit 21 of the support server 20 executes the acquisition process of the actual result corresponding to the prediction (step S1-4).
Next, the control unit 21 of the support server 20 executes the model update process (step S1-5). Here, when the published comprehensive information (updated information) is acquired, the hierarchical Bayesian model is updated.

(Outline of data used in this system)
The outline of the module and the data used in this system will be described with reference to FIG.
First, the interest rate forecasting unit 211 calculates the zero coupon yield curve and the discount factor by using the public information by the zero coupon yield curve creation logic 31. Here, the zero coupon yield curve and discount factor of each currency specified in the IRRBB regulation are calculated. Then, the interest rate forecasting unit 211 uses the interest rate forecasting model 32 (the zero coupon yield curve and the zero coupon yield curve of the Japanese yen at the start of the forecast calculated from the discount factor and the macroeconomic index which is public information. Introduce to the hierarchical Bayes model). As a result, the probability distribution of the zero coupon yield at any time point is calculated.

Next, the core deposit forecasting unit 212 calculates the probability distribution of zero coupon yield at any time point, the historical liquidity deposit interest rate, and the liquidity deposit balance by individual / corporation, in the core deposit estimation model 33 (hierarchical Bayes model). Introduce to. As a result, the core deposit amount for each period bucket is calculated.

Next, the time deposit forecasting unit 213 determines the probability distribution of zero coupon yield at any time point, the core deposit amount for each period bucket, the historical time deposit interest rate by contract period, and the balance, and determines the time deposit amount estimation model 34 ( Introduce to the hierarchical Bayes model). As a result, the fixed deposit amount for each period bucket is calculated.

Further, the prepayment rate prediction unit 214 introduces the total principal, the number of contracts, the average value, the standard deviation, and the quantile into the fixed interest rate loan prepayment rate estimation model 35 (hierarchical Bayesian model) for each period bucket. As a result, the prepayment rate for each period bucket is calculated.
The risk calculation unit 215 introduces the core deposit amount for each period bucket, the fixed deposit amount for each period bucket, and the prepayment rate for each period bucket into the interest rate risk index calculation module 36. As a result, the risk assessment result is calculated. As a risk assessment result, the interest rate of the entire portfolio, the fluctuation of net assets by shock scenario (ΔEVE), and the fluctuation of net interest income (ΔNII) are calculated.

Then, the hedge simulation unit 216 executes the simulation process by the hedge position simulator 37.

(Zero coupon yield curve creation logic)
Next, the zero coupon yield curve creation logic will be described with reference to FIG. Here, the future of the zero-coupon yield curve of the Japanese yen currency is predicted, and this yield curve is expanded to any currency.

First, the control unit 21 of the support server 20 executes an acquisition process of information on the swap rate curve and the currency swap rate (step S2-1). Specifically, the interest rate forecasting unit 211 of the control unit 21 acquires information on the swap rate curve and the currency swap rate prepared in advance.

Next, the control unit 21 of the support server 20 executes a zero coupon yield curve creation process for each currency (step S2-2). Specifically, the interest rate forecasting unit 211 of the control unit 21 creates a zero coupon yield curve for each currency to be considered in the calculation of IRRBB from the acquired information. Next, the interest rate forecasting unit 211 calculates the discount rate for each period bucket.

Next, the control unit 21 of the support server 20 executes the discount rate calculation process for each period bucket (step S2-3). Specifically, the interest rate forecasting unit 211 of the control unit 21 repeats the calculation of the discount rate from the zero coupon yield curve of each currency using the interest rate forecasting model described later. If the zero-coupon yield curve is estimated based on the maturity of the OIS (overnight index swap) swap rate, B-spline approximation is used to calculate the value of the central maturity of the period bucket. Performs linear interpolation by.

(Interest rate forecast model)
Next, the interest rate forecast model will be described with reference to FIG. This interest rate forecasting model predicts the future of the zero-coupon yield curve of the Japanese yen currency at a certain point in time, and expands the yield curve to any currency.

First, the control unit 21 of the support server 20 executes the macroeconomic index acquisition process (step S3-1). Specifically, the interest rate forecasting unit 211 of the control unit 21 acquires a macroeconomic index used for the hierarchical Bayes model from the public information storage unit 22.

Next, the control unit 21 of the support server 20 executes the acquisition process of the zero coupon yield curve of the Japanese yen at the start of the prediction (step S3-2). Specifically, the interest rate forecasting unit 211 of the control unit 21 acquires the Japanese yen zero coupon yield curve calculated in step S2-2.

Next, the control unit 21 of the support server 20 executes the prediction processing of the future zero coupon yield curve (step S3-3). Specifically, the interest rate forecasting unit 211 of the control unit 21 predicts the future interest rate curve from the hierarchical Bayesian model. Here, a hierarchical Bayesian model that adopts the Nelson-Siegel model is used. The parameters are β_1, β_2, β_3 for expressing the level, slope, and curvature, respectively, λ required as a common parameter, the number of elapsed months m (no estimation of m is required), β_1, β_2, β_3 as the following linear Gaussian. Estimate with a model. In addition, "_" means a subscript.
The state variable x_t, H is the value obtained from λ calculated by the Nelson-Siegel model and the number of elapsed months, and macroeconomic indicators (base loan interest rate, consumer price index (excluding fresh products) compared to the same month of the previous year, US financial securities (10 years) Yield, US FF rate, TSE stock index, Mining and industry production index compared to the same month of the previous year) is used. If the abbreviations are BDR_t-1, CPI_t-1, US_10t-1, FF_t-1, TOPIX_ (t-1, IIP_ (t-1)) in order, β_1t, β_2t, and β_3t can be described by the following equations.

At this time, the hyperparameters are error terms ω_t, υ_t, μ_t, α, γ included in the state model, and a to f that act as “coefficients for explanatory variables” of the state model. Let ω_t, υ_t, and μ_t be normal distributions N (0,10) assuming no information. Other hyperparameters (assumed to be hp) when the data observation start is t = 1 are calculated by the following method. This reflects the time-series structure to which the probability distribution of the parameter in the previous period is applied as the average of the probability distribution of the parameter in the period to be estimated except for the observation start period. In addition, "^" means a power.

The parameter λ follows a normal distribution. The estimation is performed with the settings that reflect the same time series structure as the hyperparameters other than the error term in the estimation of the above parameter β.

Next, the control unit 21 of the support server 20 executes the expansion process in an arbitrary currency (step S3-4). Specifically, the interest rate forecasting unit 211 of the control unit 21 calculates the value for each period bucket of any currency by using the zero coupon yield curve creation logic.

Next, the control unit 21 of the support server 20 executes the discount rate calculation process (step S3-5). Specifically, the interest rate forecasting unit 211 of the control unit 21 calculates a discount rate for any currency.

(Core deposit estimation model)
Next, the core deposit estimation model will be described with reference to FIG. In this core deposit estimation model, the amount of liquid deposits (core deposits) that remain without being withdrawn changes according to fluctuations in market interest rates. This is estimated by dividing it into personal deposits (further classified into non-tradable and transactional) and corporate deposits.

First, the control unit 21 of the support server 20 executes the historical liquidity deposit interest rate acquisition process (step S4-1). Specifically, the core deposit prediction unit 212 of the control unit 21 outputs a message prompting the client terminal 10 to upload a historical (assuming about 5 years) liquidity deposit interest rate. Then, the core deposit prediction unit 212 records the historical liquidity deposit interest rate uploaded from the client terminal 10 in the individual information storage unit 23.

Next, the control unit 21 of the support server 20 executes the acquisition process of the liquid deposit balance for each individual / corporation (step S4-2). Specifically, the core deposit prediction unit 212 of the control unit 21 outputs a message prompting the client terminal 10 to upload the liquidity deposit balance for each individual / corporation. Then, the core deposit prediction unit 212 records the liquidity deposit balance for each individual / corporation uploaded from the client terminal 10 in the individual information storage unit 23.

Next, the control unit 21 of the support server 20 executes an estimation process of the market follow-up rate of the liquid deposit interest rate (step S4-3). Specifically, the core deposit forecasting unit 212 of the control unit 21 uses the historical data recorded in the individual information storage unit 23 and the market interest rate follow-up rate model (hierarchical base model described later) of the liquidity deposit interest rate to flow. Estimate the market follow-up rate of sex deposit interest rates.
Here, the one-month zero coupon rate is set as the market-procured interest rate, and the liquid deposit interest rate and fixed deposit are used using the market-procured interest rate, the liquid deposit interest rate (ordinary deposit interest rate, etc.), and the liquid deposit interest rate. Assume a duplicate portfolio that matches the interest rate raised. By solving this, a hierarchical Bayesian model for estimating the follow-up rate θ is generated and expressed by the following equation.

The follow-up rate θ follows a normal distribution with mean μ and standard deviation as hyperparameters, and both hyperparameters are models that reflect the following time series structure with the data start period as t = 1 (hyperparameters are summarized). Notated as ph).

In addition, the future liquidity deposit interest rate can be calculated by fluctuating the market procurement interest rate r_m ^ t using this hierarchical Bayesian model constructed.

Next, the control unit 21 of the support server 20 executes the prediction process of the Japanese yen zero coupon yield curve (step S4-4). Specifically, the core deposit forecasting unit 212 of the control unit 21 estimates the posterior distribution of the probability distribution of the liquidity deposit interest rate from the calculated market follow-up rate of the liquidity deposit interest rate and the interest rate prediction model.

Next, the control unit 21 of the support server 20 executes an estimation process of the posterior distribution of the liquidity deposit balance (step S4-5). Specifically, the core deposit forecasting unit 212 of the control unit 21 uses the calculated Japanese yen zero coupon yield curve and a model for predicting the future level of liquidity deposits (hierarchical base model described later) for liquidity deposits. Estimate the posterior distribution parameters of the balance.
Here, the liquid deposit amount M_t in the future period t is expressed by a hierarchical Bayesian model based on the AR1 structure.

The parameter κ is affected by liquidity interest rates, macroeconomic indicators, and adjustment terms set for each financial institution. If the macroeconomic indicator is ρ_i, it can be expressed by the following formula.

Hyperparameters a and b_i, which act like constant terms I and coefficients of macroeconomic indicators, are as follows when the start of data observation is t = 1 (assumed to be hp. Read for each hyperparameter). Calculate by the method. This reflects the time-series structure to which the probability distribution of the parameter in the previous period is applied as the average of the probability distribution of the parameter in the period to be estimated except for the observation start period.

Next, the control unit 21 of the support server 20 executes the estimation process of the core deposit amount by the model (step S4-6). Specifically, the core deposit prediction unit 212 of the control unit 21 sets the 99% lower limit of each period bucket calculated from the posterior distribution as the core deposit amount for the period.

Next, the control unit 21 of the support server 20 executes the adjustment process of the period bucket allocation rate (step S4-7). Specifically, the core deposit prediction unit 212 of the control unit 21 calculates the core deposit distribution rate for each period bucket from the calculated core deposit amount for each period bucket, and calculates the average remaining period of the core deposit from this. If this value exceeds the upper limit of the average remaining period of the deposit type stipulated in the regulation, it is gradually decreased from the core deposit distribution rate of the longest period bucket, and the average remaining period is adjusted so as to match the upper limit of the regulation.

Next, the control unit 21 of the support server 20 executes the adjustment process of the total amount of core deposits (step S4-8). Specifically, the core deposit forecasting unit 212 of the control unit 21 determines that the total core deposit amount, which is the sum of the estimated core deposit amounts for each period bucket, exceeds the upper limit of the core deposit amount ratio to the liquidity deposits stipulated in the regulations. , Decrease the total amount of core deposits so that the ratio of core deposits matches the upper limit.

Next, the control unit 21 of the support server 20 executes the distribution process of the core deposit to the period bucket (step S4-9). Specifically, the core deposit prediction unit 212 of the control unit 21 multiplies the total core deposit adjusted in step S4-8 by the core deposit distribution rate for each period bucket adjusted in step S4-7, and buckets for each period. Distribute core deposits to.

(Time deposit amount estimation model)
Next, a fixed deposit amount estimation model will be described with reference to FIG. 7. In this fixed deposit amount estimation model, the balance of fixed deposits fluctuates according to fluctuations in market interest rates. This is estimated for each contract period, the cancellation amount of the time deposit is calculated for each term bucket, and it is redistributed to the appropriate term bucket.

First, the control unit 21 of the support server 20 executes the acquisition process of the historical fixed deposit interest rate for each contract period and the balance (step S5-1). Specifically, the time deposit prediction unit 213 of the control unit 21 outputs a message prompting the client terminal 10 to upload the time deposit interest rate for each contract period and the time deposit balance for each contract period. Then, the time deposit prediction unit 213 records the historical time deposit interest rate for each contract period and the time deposit balance for each contract period uploaded from the client terminal 10 in the individual information storage unit 23.

Next, the control unit 21 of the support server 20 executes the calculation process of the fixed deposit interest rate follow-up rate (step S5-2). Specifically, the time deposit prediction unit 213 of the control unit 21 uses the historical data uploaded by the user and the market interest rate follow-up rate model of the time deposit interest rate (hierarchical Bayes model described later) to use the market follow-up rate of the time deposit interest rate. To estimate.

Procurement consisting of fixed deposit interest rate and fixed deposit interest rate using the zero coupon rate of the period bucket including the contract term of the fixed deposit pool as the market raising interest rate and the follow-up rate of the fixed deposit interest rate and the fixed deposit interest rate. Assume a duplicate portfolio that matches the interest rate. It is a hierarchical Bayesian model that estimates the follow-up rate θ by solving this, and is expressed by the following equation.

The follow-up rate θ is a model that reflects the following time-series structure, with the mean μ and standard deviation as hyperparameters, and both hyperparameters having the data start period as t = 1. Notated as ph).

In addition, the future fixed deposit interest rate can be calculated by changing the market procurement interest rate r_m ^ t using this hierarchical Bayesian model constructed.

Next, the control unit 21 of the support server 20 executes the prediction process of the Japanese yen zero coupon yield curve (step S5-3). Specifically, the time deposit prediction unit 213 of the control unit 21 estimates the posterior distribution of the probability distribution of the time deposit interest rate from the calculated time deposit interest rate follow-up rate and the interest rate prediction model.

Next, the control unit 21 of the support server 20 executes the estimation process of the posterior distribution of the time deposit balance (step S5-4). Specifically, the time deposit prediction unit 213 of the control unit 21 estimates the posterior distribution parameter of the time deposit balance using the predicted Japanese yen zero coupon yield curve and the time deposit amount model (hierarchical Bayes model described later). To do.
The fixed deposit amount M_t in the future period t is expressed by a hierarchical Bayesian model based on the AR1 structure.

The parameter κ is affected by the fixed deposit interest rate, macroeconomic indicators, and adjustment terms set for each financial institution. If the macroeconomic indicator is ρ_i, it can be expressed by the following formula.

Hyperparameters a and b_i, which act like constant terms I and coefficients of macroeconomic indicators, are as follows when the start of data observation is t = 1 (assumed to be hp. Read for each hyperparameter). Calculate by the method. This reflects the time-series structure to which the probability distribution of the parameter in the previous period is applied as the average of the probability distribution of the parameter in the period to be estimated except for the observation start period.

Next, the control unit 21 of the support server 20 executes the process of allocating the fixed deposit amount to the period bucket (step S5-5). Specifically, the time deposit prediction unit 213 of the control unit 21 calculates the time deposit amount of the period bucket by totaling the time deposit amount for each elapsed period from the posterior distribution for each period bucket.

(Fixed interest rate loan prepayment rate estimation model)
Next, a fixed interest rate loan prepayment rate estimation model will be described with reference to FIG. In this fixed-rate loan prepayment rate estimation model, the prepayment rate of fixed-rate loans, especially those in which the incentive for prepayment is likely to change due to fluctuations in market interest rates, is estimated. The specific positions assumed are for relatively long-term certificate loans such as mortgages and investment mortgage loans.

From the perspective of extreme frame transactions such as card loans and maintaining relationships with financial institutions, business loans that are difficult to take actions such as refinancing are not included.

First, the control unit 21 of the support server 20 executes a process of acquiring summary data of total principal, number of contracts, average value, standard deviation, and quantile for each data item (step S6-1). Specifically, the prepayment rate prediction unit 214 of the control unit 21 outputs a message prompting the client terminal 10 to upload the summary data. As summary data, the following data items for each period bucket corresponding to the contractual remaining period (maturity of contracted repayment in the case of a fixed interest rate contract for the entire period, interest rate change time in the case of a fixed interest rate for a fixed period or a floating interest rate) To use. Here, for each data item, total principal, number of contracts, average value, standard deviation, quantile (10% point, 20% point, 30% point, 40% point, 50% point, 60% point, 70) % Point, 80% point, 90% point) summary data is used. As data items, the principal balance, contracted interest rate, remaining months, annual income at the time of application, equity ratio at the time of application, repayment burden rate at the time of application, and prefecture where the property is located are used. Then, the prepayment rate prediction unit 214 records the summary data uploaded from the client terminal 10 in the individual information storage unit 23.

Next, the control unit 21 of the support server 20 executes the parameter estimation process of the prepayment rate estimation model (step S6-2). Specifically, the prepayment rate prediction unit 214 of the control unit 21 updates the probability distribution of the parameters estimated in advance from the observation data of the Japan Housing Finance Agency with the data uploaded by the user.
Here, it is known in practice that the time-series transition of the prepayment rate is a process close to a lognormal distribution. Therefore, a hierarchical Bayesian model assuming a lognormal distribution is constructed.
The prepayment rate (CPR) at the elapsed years t is a function consisting of the probability distribution (dCPR) and the elapsed years t.

Let m be the mean (expected value) of this dCPR and v be the variance. At this time, the relationship between the parameters μ and θ of the lognormal distribution and the expected value m and the variance v can be expressed as follows.

The expected value m is a linear combination model that uses the constant term I and macroeconomic index, annual income at the time of application, self-financing ratio at the time of application, repayment burden rate at the time of application, prefecture where the property is located (w_1 to w_j in the mathematical formula). is there.

Furthermore, it is assumed that there is an adjustment term (υ_i) due to the difference between financial institutions, and the variance v follows a normal distribution. Therefore, I, c, υ_i and μ', θ'are all hyperparameters. Of these, υ_i sets the normal distribution with no information, and μ'and θ'set the gamma distribution with no information. Other hyperparameters when the data observation start is t = 1 (assumed to be hp. Read for each hyperparameter) are calculated by the following method. This reflects the time-series structure to which the probability distribution of the parameter in the previous period is applied as the average of the probability distribution of the parameter in the period to be estimated except for the observation start period.

Next, the control unit 21 of the support server 20 executes the estimation process of the prepayment rate for each period bucket by using the updated prepayment estimation model (step S6-3). Specifically, the prepayment rate prediction unit 214 of the control unit 21 estimates the probability distribution of the prepayment rate for each period bucket and calculates the average value (CPR'). Then, using the maturity y of the period bucket for which the prepayment rate is to be calculated, the result of the following calculation is taken as the prepayment rate (CPR).

Next, the control unit 21 of the support server 20 executes the correction process of the principal for each period bucket (step S6-4). Specifically, the prepayment rate prediction unit 214 of the control unit 21 subtracts the amount obtained by multiplying the prepayment rate one period before and the principal from the principal for each period bucket calculated based on the contracted repayment. Calculated as the principal after considering prepayment. Here, all buckets are calculated in order.

(Interest rate risk index calculation module)
Next, the interest rate risk index calculation module will be described with reference to FIG. This interest rate risk index calculation module implements a method based on the standardization platform described in the final document of the Basel Committee. Depending on the user's choice, the calculation method of the position with behavioral options can be selected.

First, the control unit 21 of the support server 20 executes the sorting process of the aggregation position (step S7-1). Specifically, the risk calculation unit 215 of the control unit 21 classifies all positions in the banking account that are affected by interest rate risk into three categories: standardization, non-standardization, and non-standardization.

Next, the control unit 21 of the support server 20 executes the division processing of the positions having interest rate options (step S7-2). Specifically, the risk calculation unit 215 of the control unit 21 classifies positions that are unsuitable for standardization and have automatic interest rate options that are clearly defined in contracts and the like. However, even in the following calculations, this position is subject to various calculations as a position without interest rate options.

Next, the control unit 21 of the support server 20 executes the division process into the period bucket (step S7-3). Specifically, the risk calculation unit 215 of the control unit 21 divides the interest rate risk measurement target position into period packets. Here, the period packet is set based on the principal repayment (contractual maturity), the interest rate renewal time, and the interest payment time for other tranches.

Next, the control unit 21 of the support server 20 executes the calculation process of the zero coupon yield curve and the discount rate (step S7-4). Specifically, the risk calculation unit 215 of the control unit 21 uses the zero coupon yield curve creation logic.

Next, the control unit 21 of the support server 20 executes the cash flow calculation process of the action option position (step S7-5). Specifically, the risk calculation unit 215 of the control unit 21 calculates cash flows for the core deposit, the fixed deposit amount, the prepayment rate, and the pull / throw rate.

<Core deposit>
Regarding core deposits, the risk calculation unit 215 first classifies non-maturity deposits (NMD) as follows.
・ Retail deposit account (settlement): Regular trading account such as salary transfer or non-interest bearing account among retail deposits ・ Retail deposit (non-settlement): retail deposit account that is not a trading account ・ Wholesale If it is difficult to distinguish between settlement and non-settlement, treat it as a non-settlement account with a conservative upper limit of the core deposit ratio.
If the internal model is not used, the estimated value entered by the user is used, and if the internal model is used, NMD is distributed to the bucket for each period according to the core deposit amount calculated by the core deposit estimation model described above. To do.

<Time deposit amount>
When the internal model is not used, the risk calculation unit 215 calculates the TDRR parameter using the scenario multiplier for each interest rate shock scenario and the fixed deposit churn rate (TDRR) estimated by the financial institution. Then, the risk calculation unit 215 calculates the cash flow by multiplying the fixed deposit balance by TDRR. On the other hand, when using the internal model, the risk calculation unit 215 estimates the cash flow using the above-mentioned fixed deposit amount estimation model.

<Advance repayment rate>
When estimating the cash flow of a fixed interest rate loan with prepayment risk without using an internal model, the risk calculation unit 215 uses the scenario multiplier for each interest rate shock scenario and the actual prepayment rate provided by the user for the period. Calculate the prepayment rate for each bucket.
When estimating using the internal model, the risk calculation unit 215 uses the prepayment rate estimated using the fixed interest rate loan prepayment rate estimation model described above.
Then, the risk calculation unit 215 adds the value obtained by multiplying the principal one period before by the above prepayment rate to the principal and interest cash flow according to the original contracted repayment plan, and also adds the element of the earliest period bucket. By reducing the number of books, a principal cash flow that takes into account prepayment is created.

<Pull-through rate>
The risk calculation unit 215 calculates the pull-through rate for the commitment of the fixed interest rate loan based on the value obtained by adding [1.96σ] to the average value calculated from the historical actual value of the user. Then, the risk calculation unit 215 calculates the cash flow by multiplying the contracted repayment schedule of the fixed interest rate loan commitment as of the calculation base date by this base value.

Next, the control unit 21 of the support server 20 executes a cash flow calculation process including interest (step S7-6). Specifically, the risk calculation unit 215 of the control unit 21 calculates the amount of interest income for each period bucket of each position from the principal cash flow and reflects it in the cash flow of the period bucket corresponding to the interest accrual time.

Next, the control unit 21 of the support server 20 executes the calculation process of the present discount value (step S7-7). Specifically, the risk calculation unit 215 of the control unit 21 calculates the discount rate [exp (-R × t_k)] by using the zero coupon yield (R) for each currency and each period packet. Note that t_k represents the center point of the period packet.

Next, the risk calculation unit 215 multiplies the calculated discount rate by the cash flow for each period bucket to calculate the present discount value for each interest rate shock scenario.

Next, the control unit 21 of the support server 20 executes the calculation process of ΔNII (step S7-8). Specifically, the risk calculation unit 215 of the control unit 21 calculates the present discount value for the next 12 months (corresponding to 6 short-term period buckets).

However, here, if the cash flow is replaced by the same cash flow even after the maturity is reached or the interest rate is changed (example: liquid deposit or floating interest rate loan), the position is calculated as unchanged during the measurement period on the B / S. To do.

Then, the risk calculation unit 215 calculates the total value of the period buckets as NII. Next, the risk calculation unit 215 calculates ΔNII (revenue approach), which is obtained by subtracting the interest rate level NII of the calculation base date from the NII of the interest rate shock scenario. However, there are only two types of interest rate shock scenarios used in the calculation of ΔNII.

Next, the control unit 21 of the support server 20 executes an add-on calculation process for a position having interest rate options (step S7-9). Specifically, the risk calculation unit 215 of the control unit 21 allocates the principal of each position to the period bucket corresponding to the time when the interest rate option can be exercised for the add-on based on the position having the divided interest rate option. , Calculate separately from the cash flow created so far. Furthermore, the risk calculation unit 215 considers the implied volatility as an American option with a condition of 25% and sets the option value (A) by using the interest rate at the time of the interest rate shock scenario set for each currency and each period packet. calculate. Further, the risk calculation unit 215 similarly calculates the option value (B) at the interest rate level as of the calculation base date.
Then, the risk calculation unit 215 calculates the add-on (KAO) of the period bucket by subtracting the total of the buy positions [AB] from the total of the sell positions [AB] for each period bucket.

Next, the control unit 21 of the support server 20 executes the calculation process of ΔEVE (step S7-10). Specifically, the risk calculation unit 215 of the control unit 21 calculates the present discounted value of all period buckets, and then reflects the add-on of the position having the calculated interest rate option property. Then, the risk calculation unit 215 sets the total value of all period buckets as EVE. Then, ΔEVE (economic value approach) is calculated by subtracting the EVE of the interest rate level as of the calculation base date from the EVE of the interest rate shock scenario.

Next, the control unit 21 of the support server 20 executes the calculation process of the modified duration (step S7-11). Specifically, the risk calculation unit 215 of the control unit 21 calculates the modified duration from the present discounted value of all period buckets based on the following modified duration formula.

However, CF_ (i j) is the cash flow of the period bucket j in the interest rate shock scenario i, and D_ (adji) is the modified duration in the same scenario.

Next, the control unit 21 of the support server 20 executes the result aggregation process (step S7-12). Specifically, the risk calculation unit 215 of the control unit 21 aggregates the interest rate level as of the calculation base date, EVE, NII, ΔEVE, ΔNII, and adjusted duration for each of the six interest rate shock scenarios. Then, the risk calculation unit 215 outputs the calculation result to the client terminal 10.

(Hedge position simulation)
Next, the hedge position simulation will be described with reference to FIG. In this hedge position simulation, an example of constructing a hedge position that satisfies the conditions by presetting the target interest rate risk-related index level and the allowable level related to the possibility of exceeding it, the type of derivative to be used, and the forecast target period is presented. To do.

First, the control unit 21 of the support server 20 executes the portfolio selection process (step S8-1). Specifically, the hedge simulation unit 216 of the control unit 21 outputs a selection screen of the portfolio to be simulated on the client terminal 10. Then, the hedge simulation unit 216 acquires the portfolio selected on the selection screen of the client terminal 10.
Next, the control unit 21 of the support server 20 executes the process of creating the probability distribution of the future interest rate (step S8-2). Specifically, the hedge simulation unit 216 of the control unit 21 creates a posterior distribution of the future zero-coupon yield curve using the interest rate forecast model described above.

Next, the control unit 21 of the support server 20 executes the discount rate creation process (step S8-3). Specifically, the hedge simulation unit 216 of the control unit 21 creates a probability distribution of the discount rate using the posterior distribution of the zero coupon yield curve.
Next, the control unit 21 of the support server 20 executes the calculation process of the interest rate risk-related index (step S8-4). Specifically, the hedge simulation unit 216 of the control unit 21 uses the created future interest rate probability distribution, discount rate, and pre-calculated cash flow as interest rate risk indicators (ΔEVE, ΔNII,) for each interest rate scenario corresponding to the portfolio. Create a target value for the modified duration distribution).

Next, the control unit 21 of the support server 20 executes the portfolio search process after the optimum hedging by optimization (step S8-5). Specifically, the hedge simulation unit 216 of the control unit 21 uses the Bayesian optimization method to satisfy the simulation setting conditions and minimize the objective variable created from the present discounted value and the complexity of hedging (effect). Search for a portfolio to maximize).

<Optimal hedging strategy for ΔEVE>
The optimal hedging strategy for ΔEVE is determined by solving the following optimization problems in order. Bayesian optimization is performed by the successive approximation optimization method using Gaussian process regression.
In order to determine the period bucket to be hedged and the range of interest rate risk change of the period bucket due to the hedging, the set of α_1 to α_19 that minimizes the following objective function is calculated. The meaning of the objective function is to add a penalty term created from the fluctuation range of the present discount value for each period bucket in order to avoid excessive hedging while aiming to maximize the present discount value after interest rate hedging.

The subscript i of EVE'_i refers to six types of interest rate shock scenarios.
EVE'_i is a standardization of the posterior distribution of the present discounted value PV_i, which takes into account the interest rate hedging effect.
α_ (i1), α_ (i2),…, α_ (i19) are the range of change in interest rate risk due to hedging for each of the 19 categories in order from the shortest period bucket (O / N), from 0%. Take discrete values in 10% divisions up to 150%.
τ_ (i1), τ_ (i2), ..., τ_ (i19) are the present discounted value for each period bucket, and h_E is the reduction amount of ΔEVE by hedging.
Derivatives used for hedging are assumed to be only plain swaps, which are fixed interest rate and floating interest rate (OIS) swaps. Also, swaps between currencies are not assumed. Therefore, even if the main cause of interest rate risk is due to basis risk between currencies, this simulation assumes that only the same currency (Japanese yen) is used in the calculation.
Assuming that α_ij obtained in the above optimization problem is fully hedged by OTC plain swap where the notional amount can be set freely, the virtual position is calculated from the OIS swap rate for each period bucket and the notional amount to be hedged. Calculate the construction cost of.

<Optimal hedging strategy for ΔNII>
Here, the optimal hedging strategy of ΔNII is based on an optimization problem similar to that of ΔEVE, but the following objective function is minimized in order to determine the period bucket to be hedged and the discounted cash flow of the period bucket by the hedging. The set of α_1 to α_6 to be converted will be calculated. In addition, there are only two interest rate shock scenarios, upper and lower parallel shifts, so read as such.

<Optimal hedging strategy for modified duration>
It is necessary to calculate the present discounted value (PV) of the entire portfolio from the present discounted value of each period bucket, and divide the value calculated using the following duration formula by the PV of the entire portfolio to obtain the adjusted duration.

However, CF_ (ij) is the cash flow of the period bucket j in the interest rate shock scenario i, and D_ (adji) is the modified duration in the same scenario.
Using the D_ (adj i) calculated in this way, the following objective function is minimized. Adopting the maximum value of D_ (adj i) as the modified duration in any interest rate path, the objective function is to minimize the error between the modified duration after hedging and the preset modified duration, as a penalty term. The idea is the same as ΔEVE, except for the three points that the order of the value of the variance is matched.

Here, the above-mentioned duration calculation formula is rewritten.

Next, the control unit 21 of the support server 20 executes the process of presenting the optimum hedging strategy (step S8-6). Specifically, the hedge simulation unit 216 of the control unit 21 calculates the hedge position required to realize the optimal hedged portfolio by optimization by using the interest rate swap (exchange of fixed interest rate and floating interest rate). ..

Next, the control unit 21 of the support server 20 executes the calculation process of the interest rate risk-related index after hedging (step S8-7). Specifically, the hedge simulation unit 216 of the control unit 21 recalculates ΔEVE, ΔNII, and modified duration when the interest rate swap in the optimal hedging strategy is used. Then, the hedge simulation unit 216 outputs the calculation result to the client terminal 10.

As described above, according to the present embodiment, the following effects can be obtained.
(1) In the present embodiment, the core deposit forecasting unit 212, the time deposit forecasting unit 213, and the prepayment rate forecasting unit 214 use a hierarchical Bayesian model. The hierarchical Bayesian model reflects changes in economic conditions from the past to the present, while autonomously learning and optimizing the effects of new data (financial institution data and changes in economic conditions). It is a chain graphical model constructed by updating.
The conventional statistical model using Bayesian statistics is constructed using static information held by financial institutions from the past, and the estimation accuracy is optimized for the financial institution that provided the data. In the present embodiment, by using Bayesian update, the time series structure (dynamics) of the data is taken into consideration, the information of an arbitrary financial institution is taken in, and the estimation accuracy is optimized each time. In addition, data of all explanatory variables that build the model is indispensable for the operation of the conventional statistical model, but in this embodiment, since it is built by the Bayesian statistical method, even if there is missing information, the missing information The risk can be reasonably evaluated by using the probability distribution of. Therefore, it is possible to correspond to the information of any financial institution. Furthermore, in the conventional statistical model calculated using individual contract information, each contract information needs to include all explanatory variables, but in the present invention, even if there is missing information, a risk is taken. Can be evaluated.

By constructing a chain graphical model with a hierarchical Bayesian structure, it is possible to appropriately reflect dramatic changes in the subsequent economic situation, etc., while considering the information at the time of model construction as prior information.
Moreover, in the case of a statistical model constructed with static data, the estimation accuracy deteriorates with the passage of time after construction. In the present embodiment, since the statistical model is updated using only the newly added data, the statistical model can be updated efficiently. As a result, it is possible to quickly optimize the environment that was not assumed at the time of model construction and maintain high estimation accuracy while taking into account the transition of past data.

(2) In the present embodiment, by using the hierarchical Bayes structure, all the variables constituting the statistical model have a probability distribution. Therefore, even if you do not know the data structure, you can make a rational estimate by updating using the probability distribution of a financial institution that uses the probability distribution created in advance, or by using the prior probability distribution as it is. .. Furthermore, by adding an adjustment term that expresses the variation in characteristics of each financial institution, it is possible to make an estimate that reflects the individuality of the financial institution, such as regional characteristics and differences in management policies.
In addition, since the influence of new data can be reflected by Bayesian update, it is possible to avoid deterioration of the performance of the statistical model while maintaining the characteristics of the model before the update to some extent (while maintaining the continuity of the estimation results of the model).

(3) In the present embodiment, the control unit 21 of the support server 20 executes a process of acquiring summary data of the total principal, the number of contracts, the average value, the standard deviation, and the quantile for each data item (step S6-. 1). Then, the control unit 21 of the support server 20 executes the parameter estimation process of the prepayment rate estimation model (step S6-2). By calculating the cash flow for each claim as a summary instead of calculating it, it is possible to perform the calculation without using the contract contents of individual claims while suppressing errors.

The above embodiment may be changed as follows.
-In the above embodiment, the core deposit forecasting unit 212 to the prepayment rate forecasting unit 214 use a hierarchical Bayesian model. Other statistical models can be used, at least in part, as long as the hierarchical Bayesian model is used.
-In the above embodiment, the core deposit balance, the fixed deposit amount, and the prepayment rate are calculated. The information required to calculate the risk calculation is not limited to these.
-In the above embodiment, the client terminal 10 and the support server 20 are used for risk assessment. The hardware configuration is not limited to these.

10 ... client terminal, 20 ... risk evaluation system, 21 ... control unit, 211 ... interest rate forecasting unit, 212 ... core deposit forecasting unit, 213 ... fixed deposit forecasting unit, 214 ... prepayment rate forecasting unit, 215 ... risk calculation unit, 216 ... Hedge simulation unit, 22 ... Public information storage unit, 23 ... Individual information storage unit, 32 ... Interest rate forecast model.

Claims (4)

The Public Information Storage Department, which stores publicly available national information,
An individual information storage unit that stores individual summary information that represents indicators in a specific institution,
A risk assessment system equipped with a control unit that calculates risk indicators.
The control unit
Using the published national information, in order to calculate interest rates and institutional indicators, we generated an interest rate forecast model and an index forecast model consisting of a chain graphical model with a hierarchical Bayesian structure.
When individual summary information for calculating an institutional index is obtained from a specific institution, the index prediction model is adjusted using the individual summary information.
According to the interest rate calculated based on the interest rate prediction model, the institutional index prediction value is calculated using the adjusted index prediction model, and the risk index is calculated based on the institutional index prediction value.
A risk assessment system characterized by Bayesian updating of the index prediction model using newly released national information or newly acquired individual summary information. The risk assessment system according to claim 1, wherein the institutional index includes a core deposit balance, a fixed deposit balance, and an prepayment rate. The Public Information Storage Department, which stores publicly available national information,
An individual information storage unit that stores individual summary information that represents indicators in a specific institution,
It is a method of evaluating interest rate risk using a risk assessment system equipped with a control unit that calculates risk indicators.
The control unit
Using the published national information, in order to calculate interest rates and institutional indicators, we generated an interest rate forecast model and an index forecast model consisting of a chain graphical model with a hierarchical Bayesian structure.
When individual summary information for calculating an institutional index is obtained from a specific institution, the index prediction model is adjusted using the individual summary information.
According to the interest rate calculated based on the interest rate prediction model, the institutional index prediction value is calculated using the adjusted index prediction model, and the risk index is calculated based on the institutional index prediction value.
A risk assessment method characterized by Bayesian updating of the index prediction model using newly released national information or newly acquired individual summary information. The Public Information Storage Department, which stores publicly available national information,
An individual information storage unit that stores individual summary information that represents indicators in a specific institution,
It is a program for evaluating interest rate risk using a risk assessment system equipped with a control unit that calculates risk indicators.
The control unit
Using the published national information, in order to calculate interest rates and institutional indicators, we generated an interest rate forecast model and an index forecast model consisting of a chain graphical model with a hierarchical Bayesian structure.
When individual summary information for calculating an institutional index is obtained from a specific institution, the index prediction model is adjusted using the individual summary information.
According to the interest rate calculated based on the interest rate prediction model, the institutional index prediction value is calculated using the adjusted index prediction model, and the risk index is calculated based on the institutional index prediction value.
A risk assessment program characterized in that it functions as a means for Bayesian update of the index prediction model using newly released national information or newly acquired individual summary information.

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