JP2003150780A - Proper premium calculating method in lifetime loan guarantee merchandise with financial asset as security, computer program for performing such method in computer, and recording medium with the program recorded - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a premium calculating method which reduces a risk at a side for paying loan proceeds when the loan proceeds payment side takes a risk for a drop below the security of financial assets at the point of time for settlement in the case of paying prescribed lifetime loan proceeds to a customer. SOLUTION: The plurality of customers are virtually assumed in simulation. Interest to be applied in each period is estimated and the total of the present value of the load proceeds to be paid to the customer till the time point of settlement with the present value of the financial assets in the case of adjustment is obtained through the use of the estimated interest. Then, the expectation value of the present value is calculated at the payment side. The total of the loan proceeds of each customer including premium at each period at the time point of settlement is obtained by using a prescribed interest and, then, an assumed settlement money amount of each customer at the time point of settlement is calculated. The value of the financial assets of the customer is calculated in the case of settlement through the use of the prescribed interest and the present value of a money amount which is smaller between the assumed settlement money amount and the value of the financial assets is calculated so that the value of premium is decided.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of calculating an appropriate premium in a lifelong loan guarantee product secured by financial assets, a computer program for causing a computer to execute such a method, and a recording medium having the program recorded therein. Regarding

[0002]

2. Description of the Related Art As an aging society progresses, the development of new financial products related to the utilization of assets of elderly households is now drawing attention. Moreover, concerns over the public pension system due to the declining birthrate and problems with long-term care have become prominent, and it is necessary to reassess the asset management method including making funds until reaching the old age.

Under such a background, many financial institutions centering on insurance companies provide various financial products that meet the customer's needs of “making funds to supplement the shortage of public pensions”. In particular, for existing products, the demand for individual annuity insurance provided by life insurance companies is increasing rapidly. To alleviate the economic unrest of elderly households, it is necessary to guarantee that they can receive a certain amount of pension for life as well as public pension. However, there are many existing products such as individual pensions that have some restrictions or conditions at the time of subscription, funded period, cancellation, and products for which the annuity payment period needs to be decided at the time of contract. In the case of insurance company products, if an insurance company goes bankrupt during the funding period, this insurance money will not be covered by deposit insurance like bank products. There is also concern that you may lose it before you start using it.

Reverse mortgage is one of the products for meeting such social needs. reverse·
Mortgage is the income obtained by continuing to live in a house that has paid off the loan, receiving a loan with the real estate as collateral, and disposing of the collateral real estate at the end of the contract period.
It is a financial product that repays the loan funds in a lump sum. A feature of reverse mortgages is that the contractor retains the ability to redistribute flow and stock assets in their lives. It is also a product with a value recreating function that redistributes cash generated from residential assets to new expenditures. For this reason, reverse mortgage is considered to be an effective means of utilizing the assets of elderly households in the aging society in the future, and it can be said that it has social benefits.

The present inventors have shown a new direction of reverse mortgage that is easier to use by limiting the risks that the elderly must bear as much as possible, and derived an evaluation model thereof. In other words, in this reverse mortgage valuation model, financial institutions bear all risks of collateral breakage, and the customer pays insurance premiums in return.Therefore, the inherent risks can be clearly explained to the customer. it can. In addition, you can expect lifelong security by paying insurance premiums, and you can continue to live in your familiar home until the contract expires or you die.

[0006]

On the other hand, on the other hand, due to the recession after the burst of the bubble, the lifestyles of people have changed, and there is an increasing tendency to choose the so-called lifetime rental type. Even if you own a home, the real estate value is low and in many cases it is not covered by collateral. Reverse mortgages cannot be used for these customer segments, and new product development is desired.

Therefore, the present invention aims to provide a new financial product for backing up life after retirement, in other words, an asset management product that complements public pensions and corporate pensions that support life after retirement. Instead of collateralizing other new financial assets, the loan provider bears all risk of collateral breakage, and in return the customer pays a premium as insurance premium, thereby providing the loan to the customer (The risk that the collateral will not be incurred by the customer, and the side providing the loan will bear the risk, in return for the customer to bear the premium equivalent to the insurance premium for reducing the risk, This makes it possible to provide loans to customers; even if there is a loss in part and the provider of the loans bears the losses, business relationships with multiple customers A scheme that makes it possible to cover those losses with the total amount of premiums to be acquired), a method of calculating an appropriate amount of premiums to be paid by the customer at that time, a computer program for causing a computer to execute such a method, and A recording medium having the program recorded therein is proposed.

[0008]

Therefore, according to the configuration of the present invention, when a customer is provided with a lifetime loan guarantee product with financial assets as collateral, the computer executes a simulation to calculate an appropriate premium value. A method of prompting input of attributes of a customer to be a loan target, loan conditions, attributes of a financial asset to be cleared in the future,
A step of estimating the death points of a plurality of virtual customers in the simulation, and a liquidation point defined at the estimated death point occurring during the loan setting period of the customer or the maturity thereof, whichever comes first, in the same simulation. And the step of estimating the interest rate applied to the period from the present time to each loan point in the period up to and the interest rate applied to the period from each loan point to the liquidation point, and using the above estimated interest rate , A step of calculating the expected value of the present value of the payment side by obtaining the total value of the present value of the loan money paid to the customer until the time of liquidation and the present value of the financial asset at the time of liquidation, and Each customer by using the interest rate (the above estimated floating rate or fixed interest rate applied for the period from each loan point to the liquidation point, which is determined by the contract setting) The step of calculating the total loan amount including the premium for each period at the time of the above liquidation and calculating the expected liquidation amount of each customer at the time of the above liquidation, and the predetermined interest rate (applied to the financial assets to be collateral Depending on the difference in interest rates, there are roughly two types of differences: fixed interest rates and estimated floating interest rates between the present time and the time of liquidation), and the step of calculating the value of the financial asset of each customer at the time of liquidation, The step of calculating the present value of the expected value of the receiving side and the present value of the receiving side and the present value of the receiving side The basic feature is to execute a step of determining an appropriate premium value from an expected value of value.

[0009] Here, financial assets refer to financial assets to be paid with some profit added in the future by the operation of an arbitrary person. For example, a fixed deposit (in this case, the principal is guaranteed, variable interest rates and fixed interest rates are fixed). Interest rates accrue) and claims (principals are not always guaranteed, but usually interest rates are fixed interest rates). However, it is not limited to these as long as it has the above properties.

The configuration according to claim 2 more specifically defines the above configuration. That is, when providing a customer with a lifetime loan guarantee product with financial assets as collateral, it is a method of calculating an appropriate value of the premium required by causing a computer to execute a simulation. Conditions, a step of prompting for the input of attributes of financial assets to be cleared in the future, and a step of estimating the death points of a plurality of virtual customers on a simulation based on a predetermined death age estimation model defined as a survival probability. , Based on a predetermined interest rate period structure model, the current time in the period until the liquidation time defined by the estimated death time that occurs during the loan setting period of the above customer or the maturity of the same, which is the same as in the simulation. To the period of interest from the time of each loan to the time of each loan and the period from the time of each loan to the time of liquidation Estimating with applicable interest, using the estimated rate,
A step of calculating the expected value of the present value of the payment side by obtaining the sum of the present value of the loan to be paid to the customer until the time of liquidation and the present value of the financial asset at the time of liquidation; Using the interest rate, calculate the total loan amount including premium for each period at the time of each liquidation of each customer, calculate the expected liquidation amount of each customer at the time of liquidation, and use the predetermined interest rate , The step of calculating the value of the financial asset at the time of each liquidation of each customer, and the present value of the smaller of the above-mentioned assumed liquidation value and the value of the financial asset to calculate the expected value of the present value of the receiving side. Perform the calculation so that the expected value of the present value of the paying side and the expected value of the present value of the receiving side are equal,
And a step of determining an appropriate premium value based on it.

In the above structure, the framework as a lifetime loan guarantee product is such that the customer has a predetermined risk-free, lifelong (or contract maturity) period (until the liquidation point), with the financial assets as collateral. On the other hand, even if there is a risk of collateral breakage at the time of liquidation, the side that pays the loan will be covered by the premium as insurance premium (collected from the customer), Ultimately, at the time of liquidation, the maximum value of the financial asset at that time will be the limit (at that time, if the sum of the loan amount including interest using the above estimated interest rate and the above premium is less, the amount will be capped , And receive it as liquidation money.

Even in the case where the loan payer suffers a loss due to collateral breakage in individual transactions with the customer, the loss is covered by premiums as insurance premiums collected in a plurality of transactions. If you smooth everything,
The premium must be set so that the collection of the premium will not ultimately result in a loss. Therefore, how to calculate the premium is the key (the characteristic of the optimum premium calculating method of the present application is there).

Here, if the payment amount on the payer side (which will be described later as the expected value P _F of the present value on the payer side as will be described later) is sorted out, the payer side pays the above value. You must continue to pay the loan until the time of liquidation, and the principal of the financial assets you have taken as collateral and an arbitrary interest rate (for example, the above estimated interest rate that is the spot rate minus a certain interest rate as a fee for financial institutions) Must be paid at the time of liquidation.

However, these are discounted at a predetermined discount rate in order to restore the present value. Moreover, since the estimated interest rate cannot be fixed for these payments, it is expressed as an expected value.

On the other hand, if the amount of money received by the payer of the loan (which will be explained later as expected value P _R of the present value of the money of the receiving side, as will be described later) is sorted out, this person is targeted at the time of the first contract. It receives financial assets as collateral from customers and puts them into operation. At the time of liquidation, it receives the amount obtained by adding a predetermined interest rate to the amount of loans to the target customers. However, as mentioned above, it is the framework of this product that the target customer does not have any extra expense other than the above collateral, so the total amount of financial assets deposited as collateral and arbitrary interest rates added to it is limited. Become. Therefore, the smaller one is the smaller one.

Since the side that pays the loan is responsible for such risks, in the configuration of the present application, at the time of liquidation, in addition to the amount that has been loaned to the target customer up to now with a predetermined interest rate, the premium as the insurance premium To collect. To be precise, the premium of each assumed customer for each period at the time of liquidation will be added to the sum of the loan amount up to that point and the respective interest rates from the time of each loan to the time of liquidation.

However, except for the principal of the financial asset, it is discounted at a predetermined discount rate to restore the present value. Moreover, since the estimated interest rate cannot be fixed for these payments, it is expressed as an expected value.

It is the break-even point on the loan payer side that the payment amount and the receipt amount on the loan payer side arranged as described above are equal.

However, in the above framework, the side that pays the loan risk bears the following risks.
That is, the risk includes "longevity risk" that the customer must continue to pay by living long, and "interest rate risk" that causes the value of the financial asset to fluctuate due to fluctuations in interest rates.

In the structure of the present application, assuming these risk models, the future price and the probability of becoming the price are estimated (the probability distribution of the future price is determined). However,
Since the above interest rate and the time of death of the customer are independent, it is extremely difficult to calculate the probability distribution when these factors work at the same time as a mathematical formula. Therefore, many virtual customers are created on a computer, the death points of those customers are estimated by the method described later, and the applicable interest rate is calculated by an arbitrary interest rate period structure model. And calculate the applicable interest rate. Specifically, a model suitable for each (interest rate, time of customer death) is created, and by simulation, a plurality of interest rate fluctuation paths are created, as described later, and at the time of customer death or contract maturity (above). The characteristic is that the interest rate up to the time of liquidation is estimated by making the corresponding
Interest rates are estimated.

By establishing a plurality of virtual customers and estimating the interest rate by executing the above simulation, the above-mentioned break-even point is calculated, whereby the optimum premium in the simulation is calculated.

On the other hand, the method of collecting the premium is roughly classified into a case where the premium is regularly collected (automatic loan; actually, it is considered to be collected at the time of liquidation) and a case where the premium is added There are cases.

Of these, claim 3 defines the former collection method, and includes the total loan amount at the time of liquidation of each customer using the above estimated interest rate and the premium to be accumulated by each customer for each period. It is characterized in that the assumed clearing money calculation step is executed by obtaining the total.

[0024] Further, in claim 4, the latter collection method is defined, and a fixed interest rate including a premium is used,
It is characterized in that the assumed clearing money calculation step is executed by obtaining the total loan amount of each customer at the time of clearing.

[0025] In claim 5, the latter collection method is also stipulated, and the total loan amount at the time of liquidation of each customer is obtained by using the interest rate obtained by adding the premium interest rate to the estimated interest rate. Then, the assumed clearing money calculation step is executed.

[0026] In claim 6, the latter collection method is also defined, and an arbitrary level is preset for the estimated interest rate, and when the estimated interest rate is at any of these levels, the The assumed clearing amount calculation step is executed by obtaining the total loan amount of each customer at the time of clearing, using a fixed interest rate including the premium determined in step 1.

In estimating the point of death of the customer,
It is possible to estimate the future death point of each customer on the simulation based on a predetermined death age estimation model defined as the survival probability (claim 2). Furthermore, in estimating the future death time of each customer based on the death age estimation model, for example, a predetermined number of uniform random numbers are generated in the computer, and each random number is made to correspond to a predetermined number of virtual target customers. That is, each random number is applied to the survival probability of the life table as described later, and the corresponding survival age is set as the future death time of each customer, thereby estimating the future death time of each customer on the simulation. (Claim 7).

On the other hand, as the interest rate period structure model used for estimating the interest rate, the Vasicek model and the Hull-White model are used in the embodiments described later, but there is no particular limitation and they are generally used. It can also be used.

It is possible by collecting the premium calculated by the above configuration from the target customer (including the case where it is collected as a fixed amount in addition to being collected as a variable interest rate or a fixed interest rate). The lifelong loan guarantee product secured by the new financial asset has the following features. It is a loan that provides living funds for the elderly, and the subscription period can be freely arranged. It is a product that deposits a lump sum payment for retirement and real estate sale / stock sale / heritage inheritance as a time deposit (or purchases bonds; financial assets), and continuously finances living funds by using them as collateral. The customer can freely select the contract period and contract start date, and can arbitrarily set the contract period. And during the contract period,
You can receive a pre-determined amount on a regular basis until the time of death or the maturity date. The customer bears no additional costs other than the pledged collateral. Collateral is cleared when the customer dies or the contract expires (clearing point), but if the collateral value is higher than the clearing price, a certain percentage of that value is returned to the surviving family or the principal. . Even if you cancel your contract in the middle of the period, you will be guaranteed the total amount of loans and the portion corresponding to interest and insurance premiums deducted from the principal. Insurance products such as pension insurance and medical insurance have a risk that the fund will not be repaid if the insurance company goes bankrupt during the funded period, but the side that pays the loan is the financial institution and the time deposit that is a product of the financial institution. In this case, the deposit insurance mechanism will guarantee the refund of the deposit up to the principal amount of 10,000,000,000 yen and the interest due to the payoff.

For the customer, there is no risk that the loan will be terminated during the contract, so compared to the existing insurance products and investment trust products for the aging society described above, products that meet the needs of the customer side. Can be said. In other words, the customer does not have to worry about terminating the loan or reducing the loan due to the collateral breakage, and can secure stable income until the contract expires or the time of death. In addition, by estimating the funds necessary for living after retirement in advance, calculating the shortfall after deducting the public pension, and accumulating the shortfall until the loan start date, it is possible to realize a comfortable life plan for the elderly. Is possible.

In this way, the target customer deposits his / her own financial assets in collateral (turns into a time deposit, or purchases and deposits a claim), and the person who receives the collateral receives a fixed amount of loan each period. As described above, if the framework of paying is realized, the risks of "longevity risk" and "interest rate risk" as shown in Fig. 1 occur. This product does not bear these risks to the customer, but the side that pays the loan (that is, the financial institution that provides the loan) bears it and bears a premium equivalent to the insurance premium to the customer. Will be asked. In other words, the financial institution that pays the loan bears the risk of interest rate fluctuations, the risk of longevity of the customer, and the like. May be Therefore, the total loss of the individual contracts, which is a loss for the loan payer, is collected from the customer by a premium equivalent to the insurance premium and covered by the total amount.

The contents of the lifetime loan guarantee product proposed in the configuration of the present application will be described below. Although the explanation is given from the perspective of a financial institution, it is possible to evaluate from the customer's perspective by reversing the direction of cash flow. The financial assets as collateral may be fixed-term deposits or bonds, but here, an example of constructing a model when fixed-term deposits are used as collateral will be described.

A product having such a new scheme will be evaluated from the following three points. For the payer of the loan, calculate a premium equivalent to the minimum required insurance premium (= calculation of premium at break-even point). Analyze the effects of the risks of "longevity risk" and "interest rate risk" on profit and loss, and calculate an appropriate premium for the side paying the loan. Calculate the market value of this new product at any time after the contract.

That is, the new lifetime loan guarantee product covers the above three items, and the present application provides a method of calculating an appropriate premium necessary for realizing such a product.

In the method of the present application, models for the risks of "longevity risk" and "interest rate risk" are assumed, and the future price and the probability of becoming that price are estimated.
To explain this in a little more technical terms, the probability distribution of future prices is determined by assuming some model of the interest rate level at the time of customer death. The probability distribution is the probability that a certain price will occur in the future, linked by the unit of price. By knowing this, the expected value of future cash flows can be calculated.

The basics of financial products are "future cash
The flow is converted to the present value and then the expected value is taken. " With a new lifetime loan guarantee product, knowing when a customer died can determine future cash flows, which can then be converted to present value by applying some interest rate model. The vague expression of some interest rate model means that any interest rate model does not matter. In other words, the time when the customer died (actually regarded as the survival probability) and the interest rate level are
By assuming that they are all independent (does not affect each other),
It means that different models can be created for "longevity risk" and "interest rate risk".

Therefore, in this new lifelong loan guarantee product, "longevity risk" is a standard model called a survival table, and "interest rate risk" is a model using yield spread or a model called interest rate term structure model such as Hull & White. It is premised that any existing material can be used for evaluation.

It has been stated that financial products can be evaluated if the future probability distribution is known. "Longevity risk"
The theoretical probability distribution can be calculated by assuming some model for "interest rate risk". However, it is difficult to theoretically obtain the probability distribution in the case where the liquidation value, which will be described later, is affected by the time when the customer dies or the interest rate level, such as a new lifetime loan guarantee product. Therefore, in the configuration of the present application, it is decided to use Monte Carlo simulation. The Monte Carlo simulation is a method for estimating the probability distribution of a composite model. The "time of death" and "interest level" according to the individual models of "longevity risk" and "interest rate risk" are virtually reproduced on a computer, and This is a method of estimating the probability distribution of a model combined with the result.

In the configuration of the present application, the customer's request for the product
When you enter (loan amount, term, etc.) and conditions (age, collateral value, etc.), Monte Carlo simulation outputs some information necessary for premium and risk assessment.

(1) Monte Carlo Simulation In order to evaluate a new lifetime loan guarantee product, two pieces of information, "when the customer dies" and "how future interest rates change" are required. . For this information, it is necessary to give a future value stochastically, assuming some model. Therefore, future values are assumed by the following measures.

Estimating the time of death τ To estimate the time of death of the customer, a life table as shown in Table 1 below is used. In the life table, mortality rates by age are calculated based on past data. That is, assuming that the age at the time of setting is 60 years, the survival probability for each age is estimated, such as 61 years, 62 years, and so on. In this lifetime loan guarantee product, assuming that the loan amount is calculated on a monthly basis, the survival probability by age in Table 1 is linearly divided to calculate the survival probability by age month. For example, the survival probabilities by month from the ages of 60 to 61 are as shown in Table 2 below.

[0042]

[Table 1]

[0043]

[Table 2]

The meaning of performing the Monte Carlo simulation is, for example, to virtually reproduce the future state of 10,000 virtual customers (there is no particular limitation on this number) on the computer on the computer. For example, 10,000 uniform random numbers are generated by a computer. 0 is a uniform random number
It is a number between 1 and 1, and is a random number in which values are scattered evenly between 0 and 1. In other words, when 10,000 random numbers are generated, about 90% of them have a numerical value of 0 to 0.9, and about 10% have a numerical value of 0.9 to 1. Therefore, if one of the uniform random numbers is applied to 10,000 individual customers, and the value of the uniform random number of a certain customer is 0.965, for example, that customer will die at 60 years and 7 months from Table 2. Can be expressed. In other words, by generating 10,000 uniform random numbers with a computer and making them correspond to 10,000 customers, it is possible to estimate the future death time of each customer on the simulation and Survival probability of a good customer can be matched with the survival table.

When a model such as a survival table is used, the mortality rate by age is numerically clear. That is, if some model is assumed for a certain factor, the probability distribution of the factor in the future can be generally expressed by a mathematical expression.

Then, the reason why the Monte Carlo simulation is performed in the present application is as described above.
The new lifelong loan guarantee products have large risk factors such as "longevity risk" and "interest rate risk", and although the probability distributions for these individual factors can be calculated numerically, the probability distributions when these factors work simultaneously It is extremely difficult to calculate (concurrent probability distribution) as a mathematical expression. The joint probability distribution is, for example, died at the age of 65 years and 9 months, and the interest rate at that time is 2.
It is a probability on a plurality of factors such as a probability of 6%.

Therefore, many virtual customers are created on a computer, and the death points of those customers are a survival table, and the interest rates applied to them are calculated by an interest rate period structure model. calculate. And for those individual factors, 64 to 65 years old, 3.
The number of customers who belong to the same category is counted by establishing a category such as 2% to 3.5%. Then, the count number is calculated as a ratio of the total number of people, and it is taken as the probability that the division occurs.

The estimated interest rate is to convert the amount (or other loan amount at the time of regular loan) settled at the time of the customer's death (or the maturity of the above contract period, whichever comes first) to the present value. Used for. This is a yield curve showing the relationship between interest rate and period, but since the time τ of death of each customer in the Monte Carlo simulation is given by the previous result, the time of death (or the maturity of the above contract period, whichever comes first) You can determine the yield curve for the period up to the point of arrival.

Here, the yield curve shows the relationship between the period and the interest rate level, and as shown in FIG.
The curve goes up to the right.

Several models have been proposed to estimate this yield curve. However, since the yield curve after estimation is used in the evaluation of the new lifetime loan guarantee product, it is only necessary to estimate the yield curve. , You can explain interest rate by any model.

The interest rate is the period from the present time to the time when a cash flow of periodic loan occurs, or the period from the time when the cash flow occurs to the time when the customer dies, and the time when the cash flow occurs. What is needed is the period up to the maturity of the contract. If the above yield curve is identified, the interest rate for this period can be calculated.

In the Monte Carlo simulation, the estimated interest rate or fixed interest rate is used to simulate the value of future financial assets for, for example, 10,000 customers. If a financial asset is temporarily deposited in a time deposit and the price of the financial asset is determined based on the estimated interest rate, the financial asset held by 10,000 customers is calculated by the term structure model of the interest rate on the Monte Carlo simulation. The value of is different after the first period, and the asset value S ₂ of the second period is calculated by the same method based on the varied asset value S ₁ of the first period. By repeating this process until maturity,
The transition (path) of the value of one financial asset can be applied to 10,000 customers in the simulation (or even if a path of interest rates is formed and applied to 10,000 customers). Further to this path, as shown in FIG. 3, by corresponding the tau the time of death of the customers who have previously calculated, it is possible to calculate the value S _tau financial assets at the time of death indicated by S _tau.

(2) Necessary premium In order to provide a new "lifetime loan guarantee product", the minimum required premium amount or value for the payer side is calculated. This required premium is calculated as a value such that the "expected present value P _F of the paying side" and the "expected expected value P _R of the receiving side" shown below match, and this is for the payer of the loan. Is the break-even point. That is, in the new lifetime loan guarantee product,
The cash flow is shown in. In other words, the amount paid by the party paying this loan is the loan that must continue to be paid until the time of liquidation, the principal of the financial assets taken as collateral, and an arbitrary interest rate (for example, from the above estimated interest rate that is the spot rate Subtracting a certain interest rate as a fee for financial institutions) is equivalent to. On the other hand, the amount received by the loan payment side is the same as the amount of financial assets received as collateral from the target customer at the time of the first contract (which is used for investment) and the amount that has been loaned to the target customer at the time of liquidation. Interest rates are added. However, as mentioned above, it is the framework of this product that the target customer does not have any extra expense other than the above collateral, so the total amount of financial assets deposited as collateral and arbitrary interest rates added to it is limited. Become. Therefore, the smaller one is the smaller one.

Then, the expected value of the present value of the total amount paid by the payer of the loan (the expected value P _F of the present value of the payer side) and the expected value of the present value of the total amount of money received by the same person (of the present value of the receiver side) When the expected value P _R ) becomes equal, it becomes a break-even point for the side that pays the loan, and the premium set in that case is the minimum required proper premium.

The method of collecting the premium can be broadly classified into a case where the premium is periodically collected (automatic loan) and a case where the premium is added and collected.
Here, for convenience of description, the following description will be made on the premise of the former case, and the latter case will also be described later.

A new lifetime loan guarantee product will be described below with reference to FIG. 4 by taking one as an example.

In the new lifelong loan guarantee product, if the financial assets to be collateral are fixed deposits (may be bonds),
It is a transaction that converts the cash flow of payments, which is a periodical loan in the future, and the cash flow of receipts, which is a liquidation at the time of death or contract maturity (at the time of liquidation). In such financial instruments that handle future cash flows, the future prices are generally evaluated by the expected value of the present value.

The contract maturity T of this lifetime loan guarantee product
Can be set arbitrarily, and the contract is liquidated even if the customer is alive at the contract maturity. The customer deposits a time deposit D ₀ yen as collateral at time 0 into a financial institution, and the time deposit is assumed to have an interest rate R _F (t) (compound interest) at time t. Further, it is assumed that there are n loan days including the contract maturity T, and the loan money B _i can be freely arranged at each time t _i (i = 1, 2, ..., N) according to the customer's needs. Let τ be the time of death of the customer, and the financial institution pays the loan amount B _i on the predetermined loan date t _i until the contract customer is dead (t _i <^ τ, ^ τ = τ∧T = min (τ, T)).
For financial institutions, loss of collateral may occur due to customers' longevity risk and interest rate risk.Therefore, financial institutions provide a premium equivalent to the insurance premium for this risk in the example below. It is assumed that the request is made by adding to the interest rate (floating rate) of the loan, and the additional interest rate at time t _i is represented by α _i (≧ 0). At the time of maturity T (0 <
If τ ≤ T) or death before that, at the time of death τ, the deposit as collateral will be canceled and the loan and interest received up to that point will be settled together. In addition, the liquidation time at this time is represented by ^ τ (= min (τ, T)), and the liquidation money is represented by C (^ τ).

(3) Expected value of present value P _{F on} payment side First, the cash flow (payment side) paid by a financial institution to a contract customer of a lifetime loan guarantee product will be examined. For simplification of the model, the interest rate applied to the time deposit is reviewed every lending date t _i , and the interest rate r (t
_i) (a minus constant value β a (≧ 0) from the spot rate), the rate shall be applied from time t _i to the time point t _{i + 1.} In addition, financial institutions until just before the customer to death, pay the loan money B _i for each loan date _{t i (0 = t 0 <} t 1 <
... <t _n = T). For these loans B _i , r (t _i ) + α obtained by adding the premium α to the financing interest rate r (t _i ) of the financial institution on the loan date t _i is applied. In order to simplify the model, the premium addition α is assumed to be constant (α _i = α).
In addition, since the time deposit that was the collateral will be canceled by liquidation, the principal plus the interest rate portion brought by the time deposit interest rate r (t) -β must be paid at the time of liquidation. Therefore, the expected value P _F of the present value on the paying side is calculated by the following equation 1.

[0060]

[Equation 1]

However, 1 _A (x) is a defining function, and the following equation 2
Means

[0062]

[Equation 2]

Therefore, 1 _{(ti, T]} (^ τ) takes the value 1 when this customer is alive at time t _i prior to maturity T.

Assume that the spot rate process is described by the Vasicek model as shown in the following equation (3) (in the following equation (29), the spot rate process is Hull.
Although explained in the & White model, these are all examples of the term structure model of the interest rate) and the interest rate r (t) is expressed by the following equation 4.

[0065]

[Equation 3]

[0066]

[Equation 4]

When the integral of the interest rate is set as in the following expression 5, the above expression 4 is expressed as the following expression 6.

[0068]

[Equation 5]

[0069]

[Equation 6]

{I (t), 0≤t≤T} also follows the normal distribution,
The average of the interest rate r (t) is the following equation 7, and the variance is the following equation 8
Therefore, the average of the integral I (t) of the interest rate is
The dispersion will be expressed by the following equation (10).

[0071]

[Equation 7]

[0072]

[Equation 8]

[0073]

[Equation 9]

[0074]

[Equation 10]

R (s) is a risk-free spot rate process, and what is expressed by the following formula 11 is the reciprocal of the risk-free interest rate from the present time 0 to the time t _i , that is, the discount rate. Then, further discount factor
The expected value Z (t) of exp (-I (t)) can be calculated by the following Expression 12.

[0076]

[Equation 11]

[0077]

[Equation 12]

The customer survival rate is given by the above life table, and it is assumed that the mortality rate and the risk-free spot rate process r (t) are independent.

Here, the survival function g (t) = P [τ> t] is considered, and g is assumed to be continuously differentiable. At this time, if the following expression 13 is set, P [τ> t] becomes the following expression 14.

[0080]

[Equation 13]

[0081]

[Equation 14]

In particular, when s> t, the equation 14 becomes the following equation 15, and this function h (t) is called the hazard rate. It is assumed that the hazard rate h (t) is given by the survival table.

[0083]

[Equation 15]

From the following equation (16), the above equation (1) becomes the following equation (17)
Can be calculated by

[0085]

[Equation 16]

[0086]

[Equation 17]

(4) Expected value of the present value of the receiving side P _R Next, at the time of maturity T, or at the time of death τ if the customer died before that, the cash received by the financial institution
Consider the flow (receiving side). The customer deposits the fixed deposit D ₀ as a collateral at the time of the contract with the financial institution at the time of the contract.
Also, in the event of the death from t _k-1 time between t _k time to settle together _{(t k-1 <τ ≦} t k), loan payments B _i and rate so far at that time There must be. Therefore, the amount C (^ τ) that must be settled at the time ^ τ
Is calculated by the following equation (18).

[0088]

[Equation 18]

Further, the value D (^ τ) of the time deposit that is the collateral at the time ^ τ is the following formula 19, and even if the mortgage is broken in the lifelong loan guarantee product, that part is a financial institution. , The expected value P _R of the present value on the receiving side is given by the following equation 20.

[0090]

[Formula 19]

[0091]

[Equation 20]

Here, when x _i is set as in the following equation 21, the fixed deposit and the clearing deposit are independent of each other and each has a normal distribution. Therefore, each X from the above equations 9 and 10
average m _i and variance v _i of _i becomes the following equation number 22 and number 23. Therefore, the above equation 20 becomes like the following equation 24.

[0093]

[Equation 21]

[0094]

[Equation 22]

[0095]

[Equation 23]

[0096]

[Equation 24]

The break-even point for a financial institution is when the expected value P _F of the present value on the paying side of the above equation 17 becomes equal to the expected value P _R of the present value on the receiving side of the above equation 24. If the interest rate correction value β applied to the time deposit as collateral is set in advance, it is possible to know the value of the premium α where P _F = P _R.

Next, assuming that the spot rate process is explained by the Hull & White model shown in the following equation 25, the interest rate r (t) becomes as shown in the following equation 26.

[0099]

[Equation 25]

[0100]

[Equation 26]

Since I (t) of the above equation 6 is expressed as the following equation 27, the above equation 7, equation 9, equation 17 and equation 2
Equation 2 is modified into the form of Equations 28 to 31 below.

[0102]

[Equation 27]

[0103]

[Equation 28]

[0104]

[Equation 29]

[0105]

[Equation 30]

[0106]

[Equation 31]

The merit of applying the Hull & White model is that the period structure of the spot rate at the present time can be reflected in the process (parameters can be determined so as to match the current yield curve).

In the configuration of the present application, as described above, the premium α is set so that the expected value P _F of the present value on the paying side = the expected value P _R of the present value on the receiving side. Is not immediately required, and the convergence value is changed such that the preset value of the premium α is changed and the expected value P _F of the paying side is equal to the expected value P _R of the present value of the receiving side. Finally, an appropriate premium α will be required.

The above is the method of collecting the premium by adding it to the interest rate (corresponding to (b) described later), that is, the method of collecting the premium by including it in the interest rate of the loan amount to the customer.

Here, the loan is made at an interest rate higher than the loan interest rate when there is no risk to the payer.
In this case, the method of setting interest rates also has the following valuations. (a) Financing at a fixed interest rate with an added risk component. The interest rate may change from time to time, but it is set at the time of contract. (b) Lending at an interest rate with the risk portion added to the floating interest rate. (c) When the floating interest rate exceeds a certain level, it shifts to another fixed interest rate. For shift criteria and applicable interest rates,
Determined at the time of contract.

On the other hand, it is also possible to periodically charge a predetermined premium, and this billing amount can be automatically loaned (that is, the customer combines the amount received periodically with this premium). Things will be loaned). It should be noted that this amount may change depending on the time, but it is set at the time of contract.

The configurations of claims 8 to 14 define a program that can be executed by the computer in order to cause the computer to execute the methods defined in the above claims 1 to 7.

That is, as a configuration for solving the above-mentioned problems, each processing defined in the above claims 1 to 7 is executed by utilizing the configuration of the computer, and can be read and executed by the computer. Computer programs are disclosed. Needless to say, these configurations may be provided not only as a computer program but also as a configuration of a recording medium (Claim 15) in which a program having a similar function is stored, as described later. In this case, the computer may be a general-purpose computer configuration including the configuration of the central processing unit, or may include a dedicated machine or the like for a specific process. There is no particular limitation as long as it is accompanied.

When such a program for causing a computer to execute each of the above processes is read by the computer, the same process as any one of the processes defined in claims 1 to 7 is executed. become.

By executing this computer program using existing hardware resources, the method of the present invention as a new application can be easily executed on existing hardware. Further, by recording such a computer program in the above-mentioned recording medium, it becomes possible to easily distribute and sell it as a software product. In addition to the above-mentioned format, the recording medium has a RAM
Needless to say, it may be the configuration of an internal storage device such as a ROM or a ROM, or the configuration of an external storage device such as a hard disk, and if such a program is recorded there, it is included in the recording medium specified in the present invention. Yes.

The function for executing a part of the processing described in claims 8 to 14 is a function incorporated in a computer (even if it is a function incorporated in a computer by hardware). Function may be realized by an operating system or another application program installed in the computer), and the program includes an instruction for calling or linking a function achieved by the computer. It may be.

This is because a part of each processing defined in claims 8 to 14 is substituted by a part of the function achieved by an operating system or the like, and a program or a program for realizing the function is provided. This is because modules and the like are not directly recorded, but if a part of the functions of the operating system that achieves those functions is called or linked, it will have substantially the same configuration.

[0118] The above-mentioned program can be used by itself or, as will be described later, recorded in a recording medium and distributed or sold, or transmitted by communication or the like to be transferred. .

Among them, the structure of claim 8 is a structure corresponding to the structure of claim 1, and its concrete structure is that the computer has the attributes of the customer to be loaned, the loan condition, and the finance to be cleared in the future. One of the steps of prompting for the input of the attribute of the asset, the step of estimating the death points of a plurality of virtual customers in the simulation, and the estimated death point that occurs during the loan setting period of the customer or the maturity thereof in the same simulation. Estimate the interest rate applicable to the period from the present time to each lending point in the period up to the liquidation point defined at the early arrival and the interest rate applied to the period from each lending point to the liquidation point And the current value of the financial assets at the time of liquidation, and the present value of the loan to be paid to the customer until the time of liquidation, using the estimated interest rate. The step of calculating the expected value of the present value on the payment side and the step of calculating the expected value of the payment side and the total of the loan amount including the premium for each period at the time of the above liquidation of each customer using a predetermined interest rate, The step of calculating the expected liquidation amount of each customer at the time of liquidation above, the step of calculating the value of the financial asset of each customer at the time of liquidation above using a predetermined interest rate, The step of calculating the present value of the present value of the smaller amount of the values and calculating the expected value of the present value of the receiving side, and a premium more appropriate than the expected value of the present value of the paying side and the expected value of the present value of the receiving side. And a computer program causing the steps of determining the value of

The structure of claim 9 is a structure corresponding to the structure of claim 2, and its concrete structure is as follows:
Based on the step of prompting for the attributes of the customer to be loaned, the loan conditions, and the attributes of the financial asset to be cleared in the future, and a predetermined death age estimation model defined as the survival probability, multiple virtual Based on the step of estimating the customer's death time and the predetermined interest rate period structure model, the same simulation is defined as the estimated death time occurring during the customer's loan setting period or its maturity, whichever comes first. Estimating the interest rate applicable to the period from the present time to each loan point in the period up to the liquidation point and the interest rate applied to the period from each loan point to the liquidation point, and the above estimated interest rate By using the present value of the loan paid to the customer up to the time of liquidation and the present value of the financial assets at the time of liquidation. Therefore, using the step of calculating the expected value of the present value of the payment side and the predetermined interest rate, the total loan amount including the premium for each period at the time of the above liquidation of each customer is obtained, and the above liquidation of each customer is calculated. The step of calculating the expected clearing amount at that time, the step of calculating the value of the financial asset of each customer at the time of the above clearing using a predetermined interest rate, and the smaller of the above assumed clearing amount and the value of the financial asset The step of calculating the present value of the amount of money and calculating the expected value of the present value of the receiving side, and the above-mentioned expected value of the present value of the paying side and the expected value of the present value of the receiving side are made equal. , A computer program for executing a step of determining an appropriate premium value based on the computer program.

The structure of claim 10 is a structure corresponding to the structure of claim 3, and specifically, the total loan amount at the time of liquidation of each customer using the estimated interest rate and each customer's period It is characterized in that the above-mentioned assumed clearing money calculation step is executed by obtaining the total of premiums to be accumulated for each.

The structure of claim 11 is a structure corresponding to the structure of claim 4, and more specifically, a fixed interest rate including a premium is used to obtain the total loan amount of each customer at the time of liquidation. Then, the step of calculating the assumed clearing money is executed.

The structure of claim 12 is a structure corresponding to the structure of claim 5, and specifically, using the interest rate obtained by adding the interest rate as a premium to the estimated interest rate, at the time of liquidation of each customer. It is characterized in that the step of calculating the assumed clearing money is executed by obtaining the total loan amount.

The structure of claim 13 is a structure corresponding to the structure of claim 6, and more specifically, an arbitrary level is set in advance for the estimated interest rate, and the estimated interest rate is set to any one of them. The above-mentioned step of calculating the expected liquidation amount is executed by obtaining the total loan amount of each customer at the time of liquidation using a fixed interest rate including the premium individually determined when It has a feature.

The structure of claim 14 is a structure corresponding to the structure of claim 7, and more specifically, a predetermined number of uniform random numbers are generated in the computer, and each random number is alive to match it. It is characterized in that the future death time point of each customer is estimated on the simulation by corresponding to a predetermined number of virtual target customers via the probability.

[0126] A fifteenth aspect is the above-mentioned eighth to fourteenth aspects.
The configuration of the recording medium in which the computer program described in (1) is recorded is as described above.

The computer that executes the computer program product may have one configuration (standalone computer or the like), but the invention is not limited to this. Server, etc.) such that each of the steps is carried out in a distributed manner on those computers (via an appropriate communication arrangement if necessary),
It may be set in the program.

[0128]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings. FIG. 5 shows a configuration of a computer 100 that executes an execution program of the method of the present invention by reading it from a recording medium such as a CD-ROM or a flexible disk and executing the program. As shown in the figure, the computer 100 includes a CPU 11, an internal storage device such as a RAM 12 and a ROM 13, a hard disk drive 14 and a CD-ROM connected through a system bus 10.
It has a normal configuration including an external storage device such as the drive 15, an input device such as the keyboard 16 and the mouse 17, and an output device such as the display 18 and the printer 19, and data required between them via the system bus 10. Instructions are exchanged.

When the execution program of the method of the present invention is read from the recording medium, the hard disk drive 1
Stored in 4. Then, when the program is executed on the CPU 11, an execution program storage unit 140, a user data storage unit 141, and a life table data storage unit 142 indicating survival probabilities for men and women are stored on the hard disk drive 14. Interest rate period structure storing a model of interest rate period structure and parameters used for the model (parameters input by an operator of the financial institution on the side of paying a loan described later are stored in a temporary data storage unit 145 described later) A model storage unit 143 and a mathematical formula storage unit 144 in which mathematical formulas used in this simulation are registered.
Then, a temporary data storage unit 145 for temporarily holding numerical data such as a coefficient input for use in this simulation and a calculation result of the simulation is formed.

Here, it is assumed that a simulation is carried out for the purpose of making a contract between the financial institution on the side of paying the loan and the customer receiving the loan to set the above-mentioned lifetime loan guarantee product. To do.

Then, the execution of this execution program by the CPU 11 causes the display 18 to show
A screen display as shown in FIG. 6 is made. That is, this figure is a screen display that prompts the operator of the financial institution operating the computer 100 to input the items necessary for executing the simulation regarding the target customer who executes the simulation according to the method of the present invention. Here, the form of depositing the financial asset in the financial institution is fixed to the time deposit (of course, as another example, the input item may be set as the subject of the bond). Gender, date of birth, set month which is the item of the set period in which the loan based on the contract for this lifetime loan guarantee product is executed, the expected maturity, the estimated period, the amount of financial assets to be collateral (principal of time deposit), the fixed term The data input items include the modified interest rate β of the interest rate and the loan amount (monthly loan amount). In this example, book C
As shown in FIG. 6, the number of executions of the simulation to be described later executed on the PU 11 is 1000 by default.
Although set to 0 times, this value can be changed by the operator. Furthermore, in the configuration of the present embodiment, the spot rate process is explained by the Vasicek model, and therefore the speed of return to the average a, the average interest rate level b, the volatility (standard deviation) σ, and the ) The applicable variable interest rate (floating interest rate level) r _{0 and the} like are also input items, but those that are registered in advance by the operator may be used.

When these are input by the operator, the execution program is executed by the user data storage unit 14
The input data is stored in 1.

The above Vasicek model is used because, when the interest rate r (t) fluctuates extremely from the average interest rate level b, the larger the deviation is, the more the return speed a to the average is multiplied. This is because the force of returning to the average will act, and it will correspond to the average regressivity of interest rates that tends to converge to a certain average level that is the basis of long-term passage of time.

Then, the CPU 11 is made to generate 10,000 uniform random numbers, and the life table data storage unit 142 is
Based on the life table data stored in, the survival probability is proportionally divided into periods, and each random number is made to correspond to a predetermined number of virtual target customers.
Have 0 customers estimate future death points. As the life table, those shown in Table 3 below for men and Table 4 below for women are used.

[0135]

[Table 3]

[0136]

[Table 4]

Also, the interest rate period structure model storage unit 143.
Based on the Vasicek model stored in, the period up to the liquidation time ^ τ defined at each estimated death time occurring during the hypothetical customer's loan setting period above or at the earlier of their maturities, whichever comes first. From the current time point 0 to each loan time point t in the period from the present time to the time point when a cash flow of periodic loan occurs, or from the time point when the cash flow occurs to each estimated death point of the customer
Interest is applied to a period of up to _i r (s), and to generate a path for estimating the applied rate r (s) with respect to time to clearing time ^ tau from each lending time t _i.

At this time, the interest rate period structure model storage unit 1
The above Equation 3 is read from 43, and the data of the return speed a to the average, the average interest rate level b, the standard deviation σ, and the variable interest rate level r ₀ at the time of setting are read from the temporary data storage unit 145. Estimate the interest rate after the first period. Then, the interest rate for the next period is similarly estimated from the estimated interest rate after the first period with variations, and the above operation is repeated until the maturity T of the loan setting period to express the transition of the interest rate r (t) 1.
Create one path. Replace the path created in this way with the above 1
Fit it as one of 0000, and then associate this pass with the estimated time of death for that customer,
Calculate the interest rate at the time of liquidation. And the above operation is repeated for 10,000 people.

Each estimated interest rate r obtained as described above is obtained by reading out the loan amount B _i from the user data storage unit 141 and reading out the above formula 1 from the formula storage unit 144.
(s) is used to tell the CPU 11 the present value of the loan money B _{i to} be paid to the customer from the present time 0 to the liquidation time ^ τ for each lending time t _i and the liquidation time ^ τ. The expected value of the present value of the payment side is calculated by calculating the expected value of the total of the present value of the time deposit (the sum of the interest and the principal due to compound interest) used as collateral, and in this embodiment. Calculate P _F.

Similarly, the loan amount B _i is read out from the user data storage unit 141, and the formula 18 is read out from the mathematical expression storage unit 144, from each loan time point t _i to the liquidation time point τ obtained as described above. Using each estimated interest rate r (s) applied to the period, each loan amount B _{i of} each customer at the time of the above liquidation and the interest rate r (s) and the premium α as an additional interest rate are applied to the CPU 11. In addition, the total sum of these is calculated, and the expected clearing amount C (^ τ) of each customer at the above-mentioned clearing point ^ τ is calculated.

Further, the principal D _{0 of the} fixed deposit is read from the user data storage unit 141, and the mathematical expression storage unit 144 is also read.
The above equation 19 is read from and the value D (^ τ) of the time deposit at the time of settlement ^ τ is calculated.

The number 20 is read out from the mathematical expression storage section 144, and the value D of the fixed deposit is stored in the CPU 11.
(^ Τ) or the assumed liquidation amount C (^ τ), whichever is smaller,
Based on the estimated interest rate r (s), the present value is converted into the expected value (average value for 10,000 persons in this embodiment) of the present value, and the principal D _{0 of the} time deposit is added to the expected value to obtain the _value on the receiving side. Calculate the expected value P _R of the present value.

The set value of the premium α in the above equation 18 is changed.
E, the expected value P of the present value of the payment side _F= On the receiving side
Present value expected P_RConvergence calculation so that
Finally, a proper premium α is obtained.

FIG. 7 is a flow chart showing the data input procedure of the operator when the above calculation method is executed using the computer 100. First, a screen that prompts the user to input the necessary items when executing the simulation is displayed (step S101). Next, it is checked whether or not an item is input by the operator (step S1).
02). If there is no input (step S102; No),
The process returns to step S101.

On the contrary, if there is such an input (step S10)
2; Yes), and it is further checked whether the input item is a planned value or a value within a predetermined range (step S103). If it is not the planned value or the value is not within the predetermined range (step S103; No), the acceptance of the input is rejected (step S104), and the process returns to step S101. On the contrary, when the input item is a planned value or a value within a predetermined range (step S10)
3; Yes), each data of these items is stored in the user data storage unit 141 (step S105).

Then, it is checked whether all necessary items have been input (step S106). If all the items have not been input (step S106; No), the process returns to step S101. On the contrary, if all the items have been input (step S106; Yes), the process proceeds to the calculation process of FIG.

FIG. 8 is a flow chart showing the flow of processing when the computer 100 is used to carry out the above calculation method. First, the CPU 11 generates 10,000 uniform random numbers, and the life table data storage unit 14
Based on the life table data stored in 2, the survival probabilities are proportionally divided into periods, and each random number is associated with a predetermined number of virtual target customers.
The future death points of 00 customers are estimated (step S201).

Next, the interest rate period structure model storage unit 143.
The interest rate r (s) applied from the current time point to each loan time point is calculated based on the model stored in (step S202). Similarly, based on the same model, the interest rate r (s) and [interest rate r (s) -β] applied from the present time to the above liquidation time ^ τ are calculated (step S203 of making a path of the same interest rate).

It is checked whether or not the above operation has been repeated for 10,000 persons (step S204).

If the number has not reached 10,000 (step S204; No), the process returns to step S202.

If the processing for creating the interest rate path has been performed for 10,000 persons (step S204; Yes), the loan amount B _i is read from the user data storage unit 141, and the formula 1 is stored from the formula storage unit 144. Read
Using the estimated interest rate r (s) and [interest rate r (s) -β] obtained as described above, the CPU 11 is caused to cause the CPU 11 to expect the present value P _F of the payer side (payment cash for 10,000 people). Calculate the expected value of the present value of the flow (step S205).

Then, the premium α is set to 0 (step S206), the loan amount B _i is also read from the user data storage unit 141, and the above formula 18 is read from the formula storage unit 144 to obtain the value as described above. Each estimated interest rate r (s) is added, and the premium α is added to the estimated interest rate r (s).
The expected clearing money C (^ τ) in step S20 is calculated (step S20).
7). At the same time, the equation 19 is read out from the mathematical expression storage unit 144 and the principal D _{0 of the} fixed deposit is transferred to the CPU 11.
Using the above estimated interest rate r (s), β is subtracted from the interest rate, and the interest accrued at the compound deposit from the present point to the compounding point is calculated, and the value D (^ τ) of the target customer's term deposit is calculated. Is calculated (step S208).

Then, it is checked whether or not the above operation has been repeated for 10,000 persons (step S209). 1
If the number has not reached 0000 (step S209;
No), the process returns to step S207.

If the processing for obtaining the value at the time of settlement of the assumed clearing money and the time deposit has been carried out for 10,000 persons (step S209; Yes), the settlement of the time deposit calculated for each customer of 10,000 persons The smaller value of the time value and the assumed clearing amount is discounted by the estimated interest rate r (s) above, and converted to the present value to obtain the expected value of the present value. The book value D ₀ is added to calculate the expected value P _R of the present value on the receiving side (the expected value of the present value of the cash flow received by 10,000 people) (step S210).

Further, the expected value P _F of the present value on the paying side
= Check whether or not the present value of the receiving side is the expected value P _R (step S211). If both values are not equal (step S211; No), the set value of premium α is changed (step S212), the process returns to step S207, and the above processing is repeated. If both values are equal (step S211; Yes), premium α is output as an optimum value on the screen (step S2).
12).

Although this value is the optimum value, it is estimated that the above financial institutions will have no profit or loss. Therefore, the value of the premium is adjusted appropriately so that profit can be actually put. May be.

When the above-mentioned computer 100 that has read the program for performing the above processing is used to set a contract for a lifetime loan guarantee product for a contractee having the following conditions, the value P _F on the payment side and the value on the receiving side are The value P _R ,
A simulation was performed to obtain the appropriate premium α and the probability of collateral breakage. Gender: Male Date of Birth: June 1, 1939 Set Month: January 2000 Age: 65 years and 7 months Expected Maturity: January 2035 Age: 100 years and 7 months Contract period: 35 years Life expectancy Adjustment: 10 years Principal of time deposit: 20 million yen Fixed interest rate of time deposit: 0.0000 / year Monthly loan amount: 90,000 yen / month Number of times simulation is designated: 10,000 times Vasicek model condition specification Regression speed a: 0.1000 Average value b: 0.0200 Volatility σ: 0.0100 Currently applicable floating interest rate: 0.0200 / year

The calculation result is as follows. Required additional interest rate lower limit: 999.0000 / year Loss ratio to principal: 0.0000% Maximum loss: 0 yen Average when loss occurs: 0 yen Collateral break probability: 0.0000

In the above example, the optimum premium α (lower limit of required additional interest rate) was 999.0000 / year.
The higher this premium α, the more profit for financial institutions, but the greater the cost burden for customers,
It will be an unattractive product. Therefore, here, we examined how the respective values are set to affect the minimum premium α, the probability of collateral loss, and the loss ratio.

In the lifetime loan guarantee product that can be provided by the simulation configuration of the embodiment of the present application, how to secure profit as an expected value becomes a problem. As mentioned above, the additional interest rate α as a premium is a kind of insurance premium to cover the risk of collateral breakage due to an increase in the loan amount due to longevity. This lifetime loan guarantee product is a product that aims to make an average profit by filling the loss in the event of collateral breaks by pooling this premium. For financial institutions, the premium when the expected return is 0 is the minimum required premium. Therefore, the larger the amount of time deposits used as collateral and the smaller the monthly loan amount, the lower the risk of collateral collateral, and as a result the minimum required premium is Less. Here, assuming a case of guaranteeing a loan for a very long period in which a financial institution has a large risk, that is, a loan period of 40 years from 60 years old to 100 years old, the minimum required premium α on the assumption that See the relationship between the amount of fixed deposits and the amount of loans that serve as collateral. Note that the fixed interest rate β of the fixed deposit interest rate is considered to be part of the minimum premium α when the cost of financial institutions is not considered, so here we assume β = 0 and focus on the required minimum premium α. To analyze the degree of influence. Also, in the analysis described below, the Vasicek model shown in Equation 3 above is used for the term structure of interest rates, and for the survival probability, the “life table” by age used to calculate life insurance premiums (see Tables 3 and 4 above). Based on the proportional division of the above (see), 10,000 sample paths for each future interest rate level and death point are obtained by Monte Carlo simulation. Note that taxes and financial institution costs are not considered because of the simplification of the model.

(1) Effect of age at the time of starting loan This product is, for example, under the assumption of guarantee of loans up to 100 years old, the loan period increases as the age at the time of starting loan increases, and the survival rate increases. Also increases. Here, the relationship between the size of the monthly loan amount and the minimum required premium α for each age at the time of loan initiation is investigated by Monte Carlo simulation based on the calculation conditions described in the following assumptions.

As the premise of the above calculation, gender: male, set month: January 2001, expected maturity: (age: 100 years and 7 months), time deposit amount as collateral: 20,000 thousand yen, fixed interest rate Adjusted interest rate β = 0, speed of return to average a = 0.
1, average interest rate level b = 0.02, standard deviation σ = 0.0
1. Set floating interest rate level r ₀ = 0.02 at the time of setting.

In order to analyze the influence of the age at the time of setting, that is, the influence on the length of the period until maturity, the age at the time of setting is 70 years and 7 months (30 years period), 65 years and 7 months (35 years period). ), 60 years and 7 months (40 years). Monthly loan amount from 50,000 yen to 150,000
FIG. 9 shows how the value of the minimum premium α changes depending on the age at the time of setting after changing it to 00 yen. Further, FIG. 10 shows the probability that the collateral is broken at the time of liquidation, and FIG. 11 shows the loss ratio to the total principal amount for the financial institution when the collateral is broken (a loss occurs). is there. The level of the minimum required premium α is determined by the customer's needs and the allowable range for the premium, but if the upper limit is about 3%, the upper limit of the monthly loan amount when the set age is 70 years old is set. About 117 thousand yen,
The upper limit of the monthly loan amount when the set age is 65 years old is about 102,000 yen, and the upper limit of the monthly loan amount when the set age is 60 years old is about 90 thousand yen. In addition, the probability of breaking the collateral is about 27 each.
%, About 31%, about 34%.

(2) Effect of the amount of time deposits This product can increase the monthly loan amount as the amount of time deposits as collateral increases. Under the following calculation conditions, the relationship between the size of the monthly loan amount and the minimum required premium α for each amount of time deposit is investigated by Monte Carlo simulation.

As assumptions for the above calculation, gender: male, set month: January 2001, customer age at setting: 65 years, assumed maturity: (age: 100 years and 7 months), fixed interest rate β of fixed interest rate =
0, the speed of return to the average a = 0.1, the average interest rate level b = 0.02, the standard deviation σ = 0.01, and the floating interest rate level r ₀ = 0.02 at the time of setting.

In order to analyze the influence of the amount of time deposits as collateral, the amount of money is 20,000 thousand yen, 15,0
There are three types of settings, 000 yen and 10,000,000 yen. FIG. 12 shows how the monthly premium amount is changed from 20,000 yen to 120,000 yen and the value of the minimum premium α changes depending on the amount of the fixed deposit. Also,
FIG. 13 shows the probability that the collateral is broken at the time of liquidation, and FIG. 14 shows the loss ratio with respect to the total principal amount for the financial institution when the collateral is broken.
If the upper limit of the required minimum premium α is about 3%, the maximum monthly lending amount when the time deposit is 20,000,000 yen is about 102,000 yen, and the time deposit is 15,000,000 yen. The maximum monthly loan amount is about 76,000 yen, and the maximum monthly loan amount when the time deposit is 10,000 yen is about 5 yen.
It will be 0000 yen. The probabilities of collateral breakage are about 31%, about 30%, and about 29%, respectively.

(3) Effect of standard deviation In the present application, the interest rate applied to the time deposit is the variable interest rate r.
The value obtained by subtracting the fixed interest rate β from (t _i ), the interest rate applied to the loan amount is the floating interest rate r (t _i ) plus the fixed interest rate α. In this framework, both basic interest rates are floating rates, which reduces the interest rate risk for financial institutions (of course, as mentioned above, fixed interest rates are applied to fixed deposits and loan amounts. It is also possible to apply the product). The size of the monthly loan is changed for each standard deviation σ of interest rates, and the Monte Carlo
By performing a simulation, the minimum required premium α
Clarify the relationship with.

As the above-mentioned preconditions for calculation, gender: male, set month: January 2001, customer age at setting: 65 years, expected maturity: (age: 100 years and 7 months), amount of fixed deposit as collateral :
JPY 20,000, fixed interest rate β = 0 for fixed interest rate, speed of return to average a = 0.1, average interest rate level b = 0.0
2. Set floating interest rate level r ₀ = 0.02 at the time of setting.

Standard deviation σ of the Vasicek model expressed by the equation 3
To analyze the effect of, the value is 0.005,
Three types of settings, 0.010 and 0.015 are set. FIG. 15 shows how the value of the lowest premium α changes depending on the value of the standard deviation σ while changing the monthly loan amount from 20,000 yen to 120,000 yen. In addition, FIG.
Indicates the probability that the collateral is broken at the time of liquidation,
FIG. 17 shows the loss ratio with respect to the total principal amount for the financial institution when the collateral is broken. If the upper limit of the required minimum premium α is about 3%, the upper limit of the monthly loan amount when volatility is 0.005 is about 100 thousand yen, and the upper limit of the monthly loan amount when volatility is 0.010. Is about 102,000 yen, and the maximum monthly lending amount when volatility σ is 0.015 is about 1
It will be 08,000 yen. It can be seen that as the volatility σ increases, the monthly lending amount can be set slightly higher.
The probability of collateral breakage is about 32% and about 31%, respectively.
%, About 32%, and the effect of volatility σ is small up to the monthly loan amount of about 110 thousand yen.

(4) Effect of average interest rate level In order to analyze the effect of the average interest rate level b of the Vasicek model of the above equation 3, Monte Carlo simulation is performed under the following conditions, and the minimum required premium α Reveal the relationship. In addition, the value of the floating interest rate level r ₀ at the time of setting is
It is equal to the average interest rate level b (r ₀ = b).

As the above-mentioned preconditions for calculation, gender: male, set month: January 2001, customer age at setting: 65 years, expected maturity: (age: 100 years and 7 months), amount of time deposit as collateral :
It is assumed that the fixed interest rate β of the fixed interest rate is 20,000, the return speed to the average is a = 0.1, and the standard deviation σ is 0.01.

To see the effect of the average interest rate level b,
Three levels of 0.01, 0.02, and 0.03 are set as the level. FIG. 18 shows how the value of the minimum premium α changes with the average value of the interest rate level b by changing the monthly loan amount from 20,000 yen to 120,000 yen. Further, FIG. 19 shows the probability that the collateral is broken at the time of liquidation, and FIG. 20 shows the loss ratio with respect to the total principal amount for the financial institution when the collateral is broken. If the upper limit of the required minimum premium α is about 3%, the upper limit of the monthly loan amount when the average interest rate level b is 0.01 is about 96,000 yen, and the average interest rate level b is 0. When the loan amount is 0.02, the upper limit of the monthly loan amount is approximately 102,000 yen, and the average interest rate level b is 0.0.
When it is 1, the upper limit of the monthly loan amount is about 111,000 yen.
It can be seen that the higher the average interest rate level b, the higher the monthly loan amount can be set. This is because the higher the interest rate level, the higher the value of the time deposit, and the higher the interest rate applied to the loan amount, but the time when the collateral is broken becomes longer. In addition, the probability of breaking the collateral is about 31 each.
%, About 31%, about 32%.

(5) Impact of life expectancy Although advances in medical technology may lead to an increase in life expectancy in the future, the total loan amount of this product increases as the customer's life expectancy increases, and it is a collateral for financial institutions. The risk of cracking increases. In order to see the effect, the state change of the minimum required premium α when the life expectancy increases at this moment will be clarified by performing Monte Carlo simulation under the following conditions.

As the above-mentioned preconditions for calculation, gender: male, set month: January 2001, customer age at the time of setting: 65 years, assumed maturity: (age: 100 years and 7 months), amount of fixed deposit as collateral :
JPY 20,000,000, fixed interest rate β = 0, return speed to average a = 0.1, standard deviation σ = 0.01, average interest rate level b = 0.02, floating interest rate at the time of setting Level r ₀ =
Set to 0.02.

In order to see the effect of an increase in life expectancy, the number of years is 0 years, 2 years, 4 years, 6 years,
There are 5 types of settings, 8 years. Monthly loan amount 2
FIG. 21 shows how the value of the minimum premium α changes depending on the number of years of increase in life expectancy by changing the value from 0000 yen to 120,000 yen. Further, FIG. 22 shows the probability that the collateral is broken at the time of liquidation, and FIG. 23 shows the loss ratio with respect to the total principal amount for the financial institution when the collateral is broken. If the upper limit of the required minimum premium α is about 3%, the upper limit of the monthly loan amount is about 10 when the life expectancy is 0 years.
2,000 yen, about 9 when life expectancy increases for 2 years
8,000 yen, about 9 when life expectancy increases for 4 years
2,000 yen, the maximum monthly loan amount is about 90,000 yen when the life expectancy is 6 years. As the average life expectancy increases, the total loan amount increases, and the possibility that the collateral will be broken increases, so the monthly loan amount decreases.

As described above, in the product for guaranteeing a lifetime loan,
The size of the loan amount and the level of the premium change depending on the conditions such as the amount of fixed deposit as collateral shown in (1) to (5) and the age of the customer at the time of setting. In addition, from a financial institution's point of view, although the risk of collateral breakage is covered by a premium, it is necessary to always be aware of the number of cases of collateral breakage and the size of the premium. Here, we analyzed the effects of various factors on the loan amount and premium, but these results show that the premium and loan amount can be set within a sufficiently practical range.

[0177] The configuration of the calculation method including the simulation for providing the lifetime loan guarantee product in the present embodiment detailed above sufficiently suggests that the product corresponding to the aging society in the future can be provided. It is possible to construct a pricing model based on that idea. If the model is realized, even if the collateral is broken, continuous financing to the customer during the contract period is guaranteed, and a financial product with a kind of insurance can be provided.
Customers can secure stable income until the contract expires or the time of death, without fear of the loan being cut off or the amount being reduced due to collateral breakage. On the other hand, financial institutions bear the risk of interest rate fluctuations and the risk of longevity of their customers, and in order to cover the losses due to such risks, premiums as insurance premiums are collected from their customers.

After the step of determining the value of the premium α in the configurations of claims 1 and 2, claim 8 and claim 9 of the claims, the step of outputting the determined premium α is executed. By doing so, the value of the premium α is actually provided to the customer and the party who pays the loan.

The method of calculating the appropriate premium in the lifelong loan guarantee product secured by the financial assets of the present invention is not limited to the above-mentioned embodiment, and various modifications can be made without departing from the gist of the present invention. Of course, it is possible to add.

For example, regarding how to collect a premium, when a predetermined premium is regularly billed, or when a loan is made, a loan is made at a fixed interest rate with an added risk portion, or a risk portion is added to a variable interest rate. There is a way to lend at a fixed interest rate or shift to another fixed interest rate when the floating interest rate exceeds a certain level.

The term structure model for interest rates is described above.
Other than Vasicek model and Hull & White model, Gaussian type model, Cox-Ingersoll-Ross type model, Hoo-
Lee type model, Black-Derman-Toy type model, Black-Karasinski type model, Heath-Jarrow-M
It is also possible to use an orton type model or the like.

[0182]

As described above, the first aspect of the present invention is as described above.
According to the method for calculating an appropriate premium in a lifelong loan guarantee product secured by financial assets according to claim 15, a computer program for causing a computer to execute the method, and a recording medium in which the program is recorded, the financial asset With the collateral as the collateral, the customer can obtain a predetermined loan without risk until the above liquidation time, and on the other hand, even if there is a risk that the customer who pays the loan may break the collateral at the time of the above liquidation. By covering the above with the above premium as an insurance premium, at the time of final liquidation, the maximum value of the financial asset at that time will be the limit (at that time, the above premium will be added to the total loan amount including interest using the above estimated interest rate). If the added amount is less, then that amount is the limit), and if you try to realize a new product form that receives it as liquidation, Even if the party paying the loan suffers a loss due to collateral breakage, a premium as an insurance premium is collected in multiple transactions, and it is eventually smoothed out in all transactions. It is possible to obtain an excellent effect that it is possible to calculate an optimal premium that can prevent loss.

[Brief description of drawings]

FIG. 1 is a graph showing two major risks in a lifetime loan guarantee product.

FIG. 2 is a graph showing an example of a yield curve.

FIG. 3 is a graph showing a state in which a transition (path) of one interest rate is applied to the nth customer in the simulation, and this path is associated with the time of death of the nth customer calculated previously. is there.

[Figure 4] Cash for new lifetime loan guarantee products
It is explanatory drawing which shows a flow.

FIG. 5 is an explanatory diagram showing a circuit outline of a computer 100 that executes an execution program of the method of the present invention read from a recording medium.

6 is an explanatory diagram showing an input screen displayed on a display 18. FIG.

FIG. 7 is a flowchart showing an operator's data input procedure when the computer 100 is used to execute the above calculation method.

FIG. 8 is a flowchart showing the flow of processing when the computer 100 is used to carry out the above calculation method.

FIG. 9 is a graph showing how the value of the minimum premium α changes depending on the age at the time of setting.

FIG. 10 is a graph showing the probability that the collateral is broken at the time of liquidation.

FIG. 11 is a graph showing a loss ratio with respect to a total principal amount for a financial institution when a collateral is broken.

FIG. 12 is a graph showing how the value of the minimum premium α changes depending on the amount of time deposit.

FIG. 13 is a graph showing the probability that the collateral is broken at the time of liquidation.

FIG. 14 is a graph showing a loss ratio with respect to a total principal amount for a financial institution when collateral is broken.

FIG. 15 is a graph showing how the value of the lowest premium α changes depending on the value of the standard deviation σ.

FIG. 16 is a graph showing a probability that the collateral is broken at the time of liquidation.

FIG. 17 is a graph showing a loss ratio with respect to a total principal amount for a financial institution when a collateral is broken.

FIG. 18: Interest rate level b where the value of minimum premium α is average
It is a graph which shows how it changes with the value of.

FIG. 19 is a graph showing a probability that the collateral is broken at the time of liquidation.

FIG. 20 is a graph showing a loss ratio with respect to a total principal amount for a financial institution when collateral is broken.

FIG. 21 is a graph showing how the value of the minimum premium α changes depending on the number of years of increase in life expectancy.

FIG. 22 is a graph showing the probability that the collateral is broken at the time of liquidation.

FIG. 23 is a graph showing a loss ratio with respect to a total principal amount for a financial institution when collateral is broken.

[Explanation of symbols]

10 system bus 11 CPU 12 RAM 13 ROM 14 hard disk drive 15 CD-ROM drive 16 keyboard 17 mice 18 display 19 Printer 100 computers 140 Execution program storage 141 user data storage 142 Life table data storage 143 Interest rate period structure model storage 144 Formula storage 145 Temporary data storage

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Yoshiko Murauchi             2-7-1 Marunouchi, Chiyoda-ku, Tokyo             Ceremony Company Tokyo Bank of Mitsubishi F-term (reference) 5B056 BB00 HH00    (54) [Title of Invention] A method of calculating an appropriate premium for a lifetime loan guarantee product with financial assets as collateral, and such a method.                     Computer program to be executed by computer and recording medium on which the program is recorded                     body

Claims (15)

[Claims] 1. A method of calculating an appropriate value of a premium required by causing a computer to execute a simulation when providing a customer with a lifelong loan guarantee product with financial assets as collateral, The steps of prompting for the input of attributes, loan conditions, and attributes of financial assets to be liquidated in the future, the step of estimating the death points of multiple virtual customers in the simulation, and the same simulation in the loan setting period of the above customers Interest rate applicable to the period from the present time to each loan point in the period up to the liquidation point defined at the estimated death time that occurs or at the time of maturity, whichever comes first, and from each loan point to the liquidation point The step of estimating the interest rate applicable to the period of Calculating the expected value of the present value of the paying side by calculating the sum of the present value of the loans to be paid and the present value of the financial assets at the time of liquidation, and using the prescribed interest rate, The step of calculating the total loan amount including the premium for each period at the time of liquidation and calculating the expected liquidation amount of each customer at the time of liquidation, and using the predetermined interest rate, Calculating the value of the financial asset, calculating the present value of the assumed clearing liquid or the value of the financial asset, whichever is smaller, and calculating the expected value of the present value of the receiving side; Appropriate premier in a lifetime loan guarantee product collateralized by financial assets, characterized by executing the expected value of present value and the step of determining an appropriate premium value based on the expected value of the receiving side Calculation method. 2. A method of calculating an appropriate value of a premium required by causing a computer to execute a simulation when providing a customer with a lifetime loan guarantee product with financial assets as collateral. Estimate the death points of multiple virtual customers in a simulation based on the step of prompting for input of attributes, loan conditions, and attributes of financial assets to be cleared in the future, and a predetermined death age estimation model defined as survival probability Based on a predetermined interest rate term structure model, the period up to the liquidation point defined at the estimated death point occurring during the customer's loan setting period or the maturity date, whichever comes first, in the same simulation. The interest rate applicable to the period from the present time to each loan point and the period from each loan point to the liquidation point The step of estimating the applicable interest rate, and the sum of the present value of the loan payable to the customer up to the time of liquidation and the present value of the financial asset at the time of liquidation, using the estimated interest rate. And the step of calculating the expected value of the present value of the payment side, and using a predetermined interest rate, obtain the total loan amount including the premium for each period at the time of the above liquidation of each customer and One of the steps of calculating the expected liquidation amount at the time of liquidation, the step of calculating the value of the financial asset of each customer at the time of the above liquidation, using a predetermined interest rate, and the above-mentioned expected liquidation amount and the value of the financial asset. Calculate the present value of a small amount and calculate the expected value of the present value of the receiving side, and the above calculation so that the expected value of the present value of the paying side and the expected value of the present value of the receiving side are equal. Done Appropriate premium calculation method in lifetime loan guarantees products that collateral financial assets and executes the steps of determining a proper value of the premium based on it. 3. The step of calculating the assumed liquidation amount is performed by obtaining the total loan amount at the time of liquidation of each client using the estimated interest rate and the total premium that each client should accumulate for each period. The method according to claim 1, wherein
Alternatively, a method of calculating an appropriate premium for a lifelong loan guarantee product secured by the financial asset according to claim 2. 4. The step of calculating the expected liquidation amount is executed by obtaining a total loan amount of each customer at the time of liquidation using a fixed interest rate including a premium. Alternatively, a method of calculating an appropriate premium for a lifelong loan guarantee product secured by the financial asset according to claim 2. 5. The step of calculating the assumed clearing money is executed by obtaining the total loan amount of each customer at the time of clearing by using an interest rate obtained by adding an interest rate as a premium to the estimated interest rate. A method for calculating an appropriate premium in a lifelong loan guarantee product secured by the financial asset according to claim 1 or 2. 6. A fixed interest rate including a premium that is individually determined when the estimated interest rate is set in advance and the estimated interest rate is at any of these levels, and each customer is The step of calculating the assumed liquidation amount is executed by obtaining the total loan amount at the time of liquidation of the above item. The lifelong loan guarantee product secured with the financial asset according to claim 1 or claim 2. How to calculate the appropriate premium in. 7. A predetermined number of uniform random numbers are generated by the computer, and each random number is made to correspond to a predetermined number of virtual target customers via survival probabilities that match the random numbers. A method for calculating an appropriate premium in a lifelong loan guarantee product secured by the financial asset according to any one of claims 1 to 6, wherein the future death time of the customer is estimated. 8. A step of prompting a computer to input attributes of a customer to be a loan target, loan conditions, attributes of a financial asset to be cleared in the future, and a step of estimating the death points of a plurality of virtual customers in a simulation. Similarly, on the same simulation, for the period from the current point in the period up to the liquidation point defined at the estimated death point occurring during the customer's loan setting period or the maturity date, whichever comes first, to the loan point The interest rate applied to the customer and the interest rate applied to the period from the time of each loan to the time of liquidation, and using the above estimated interest rate, Calculating the expected value of the present value of the paying side by calculating the present value and the present value of the above financial assets at the time of liquidation; Using, the step of calculating the total loan amount including the premium for each period at the time of each liquidation of each customer, calculating the assumed liquidation amount of each customer at the time of liquidation, and using a predetermined interest rate, Calculate the expected value of the present value of the receiving side by calculating the present value of the smaller of the assumed clearing amount and the value of the financial asset, which is the step of calculating the value of the financial asset of each customer at the time of liquidation And a step of determining an appropriate premium value based on the expected value of the present value of the paying side and the expected value of the present value of the receiving side. 9. Based on a step of prompting a computer to input attributes of a customer to be a loan target, loan conditions, attributes of a financial asset to be cleared in the future, and a predetermined death age estimation model defined as a survival probability. Based on a predetermined interest rate period structure model, the steps of estimating hypothetical death points of a plurality of customers in a simulation, and the estimated death points occurring during the loan setting period of the customer or the maturity thereof in the same simulation. The interest rate applicable to the period from the current time to each loan point and the interest rate applied to the period from each loan point to the liquidation point in the period up to the liquidation point defined at the earliest time Estimating steps, using the above estimated interest rate, the present value of the loan money paid to the customer until the above liquidation time, and the The step of calculating the expected value of the present value of the payment side by calculating the total with the present value of financial assets, and using a predetermined interest rate, the loan amount including the premium of each customer at the time of the above liquidation for each period And calculating the expected liquidation amount of each customer at the time of the above liquidation, the step of calculating the value of the financial assets of each customer at the time of the above liquidation using a predetermined interest rate, and the above-mentioned assumed liquidation The step of calculating the present value of the present value of the receiving side by calculating the present value of the smaller value of gold and the value of financial assets, and the expected value of the present value of the receiving side and the present value of the receiving side A computer program characterized by: performing a calculation such that the value is equal to the value, and determining a proper premium value based on the calculation. 10. The assumed clearing money calculation step is executed by obtaining a total loan amount at the time of clearing each customer using the estimated interest rate and a total premium to be accumulated by each customer for each period. The computer program according to claim 8 or 9, characterized in that. 11. Using a fixed interest rate including premium,
The computer program according to claim 8 or 9, wherein the step of calculating the assumed clearing amount is executed by obtaining the total loan amount of each customer at the time of clearing. 12. The step of calculating the expected clearing money is executed by obtaining the total loan amount of each customer at the time of clearing by using an interest rate obtained by adding an interest rate as a premium to the estimated interest rate. The computer program according to claim 8 or 9, characterized in that. 13. Each customer is provided with a fixed interest rate including a premium which is preset when an arbitrary level is set for the estimated interest rate and when the estimated interest rate is at any of these levels. 10. The computer program according to claim 8 or 9, wherein the step of calculating the assumed liquidation amount is executed by obtaining the total loan amount at the time of liquidation. 14. Each of the simulations is performed by causing a predetermined number of uniform random numbers to be generated by the computer and making each random number correspond to a predetermined number of virtual target customers through survival probabilities that match the random numbers. The computer program according to any one of claims 8 to 13, characterized in that a future death time of the customer is estimated. 15. A computer-readable recording medium on which the computer program according to claim 8 is recorded.