# Option embedded in the deposit is

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Published15 Oct Abstract Under the condition of continuous innovation of financial derivatives and marketization of interest rate, interest rates fluctuate more frequently and fiercely, and the measurement of interest rate risk also attracts more attention.

Under the premise that the fluctuation of interest rate follows fuzzy stochastic process, based on the option characteristics of financial instruments with embedded option, this paper takes effective duration and effective convexity as tools to measure interest rate risk when embedded options exist, tries to choose CIR extended model as term structure model, and uses the Monte Carlo method for hybrid low deviation sequences HPL-MC to analyze the prepayment characteristics of MBS, a representative financial instrument with embedded options, when interest rates fluctuate; on this basis, the effectiveness of effective duration management of interest rate risk is demonstrated with asset liability management cases of commercial banks.

### Embedded Options and Long-Term Interest Rate Risk: Interest Rate Risk

At the same time, the frequent fluctuation of interest rates also gives birth to various derivative financial instruments; among them, financial instruments with the characteristics of embedded options such as deposits that can be withdrawn in advance, loans that can be paid in advance, mortgage-backed securities, collateralized mortgage obligation, and callable bonds are more and more embedded in the balance sheets of commercial banks, which greatly increases the difficulty of interest rate risk management of commercial banks.

The gap model based on traditional duration and traditional convexity is less effective in interest rate risk management; therefore, it is of great significance to measure and manage the interest rate risk of embedded option financial instruments [ 2 ].

### CFA L2 FY SS 14 Reading 45 Valuation of Bonds with embedded options Part 1

Scholars at home and abroad have made some important achievements in the study of interest rate risk of embedded options. Internationally, Brent and Richard proposed the Monte Carlo MC simulation pricing method for the embedded options belonging to the Asian option type; after estimating the parameters in the model based on this method, the price of embedded option bonds was obtained [ 3 ].

Brooks made a sensitivity analysis on the value of embedded options and interest rate level in CDs based on cross-sectional data [ 4 ].

Domestic scholars have also made important achievements in the research of embedded options.

### Embedded Options in Enhanced Certificates of Deposit

Zhenlong and Hai decomposed the option characteristics of assets and liabilities in the balance sheet of commercial banks and used the basic principles of financial engineering to price implicit options without arbitrage and also made numerical pricing [ 6 ].

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Therefore, commercial banks urgently need to establish a complete interest rate risk management system in time. However, the traditional risk management methods, such as interest rate sensitivity gap and duration gap, have been unable to meet the interest rate risk management requirements of assets and liabilities with embedded options.

### Embedded Option

The review of the research results at home and abroad shows that the research on embedded options started earlier in foreign countries; although the domestic research started late, it has also made some achievements. Domestic option embedded in the deposit is studies focus on pricing the value of embedded options, but few focus on the measurement and management of interest rate risk of embedded options.

In addition, the differential equation method and nonarbitrage pricing method adopted by predecessors are based on a series of strict preconditions. The traditional Monte Carlo simulation method is usually used to calculate the price of embedded option and the effective duration of securities with embedded option; however, the random number sequence generated by traditional MC in the simulation space is unevenly distributed, which wastes a large number of observations and reduces the operation efficiency; therefore, this paper uses a more advanced simulation method, namely, HPL-MC, based on the optimized interest rate risk management tools, namely, effective duration and effective convexity, makes an empirical analysis on the change of characteristics of financial instruments caused by the existence of embedded options, and demonstrates how commercial banks can effectively measure and manage interest rate risk when implicit options exist.

Analysis on the Option Characteristics of Financial Instruments with Embedded Options With the increasing types of derivative financial instruments, financial instruments with embedded options are more and more embedded in the assets and liabilities of commercial banks, such as deposits that can be drawn in advance, prepayable loans, collateralized mortgage obligation, callable bonds, mortgage-backed securities, and so on.

Here, we will take the prepayment of housing mortgage loans as an example to illustrate. Influencing Factors of Prepayment of Housing Mortgage Loans From the perspective of borrowers, the following factors will affect their prepayment behaviors.

Interest Rate Factor The interest rate factor is the primary factor to decide the prepayment behaviors.

## Embedded Option Definition

The interest rate factor here refers to option embedded in the deposit is balance between the market interest rate and the contract interest rate: the contract interest rate determines the interest expense of the loans and the market interest rate determines the cost of refinancing.

Assuming that the borrower prepays at timethe refinancing cost is expressed bythe penalty isand the loan balance at time is is greater than zero, prepayment will be executed.

An embedded option is a feature of a financial security that lets issuers or holders take specified actions against the other party at some future time.

In addition, when the national macroeconomic operation is good, the whole real estate market is hot, and when the rise of house price exceeds the balance of mortgage loan, prepayment will appear in large number. Institutional Factors The minimum amount of prepayment and the limit of the times of prepayment will restrain the behavior of prepayment to a certain extent.

However, the penalty for prepayment of housing mortgage loan is not high in our country, that is to say, the cost of prepayment is small, so prepayment often occurs.

Other Factors Factors such as relocation, mortgage characteristics, and seasons. Positive Impact Firstly, the prepayment of housing mortgage loan reduces the possibility of nonperforming loan and reduces the credit risk.

The guidance in this bulletin is supplemental to the detailed supervisory expectations included in the "Interest Rate Risk" booklet of the Comptroller's Handbook.

Secondly, the prepayment of housing mortgage loan increases the liquidity of commercial bank assets and improves the response ability of commercial banks to long-term and short-term capital demand and the efficiency of capital utilization. Negative Effect Firstly, prepayment reduces the interest margin of deposit and loan greatly, which is the main part of profit for commercial banks, so prepayment option embedded in the deposit is reduce the profit of commercial banks.

Secondly, the risk of reinvestment of commercial banks increases; when the market interest rate decreases, commercial banks can only look for investment projects with low return rate, and the reinvestment income is greatly reduced.

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Thirdly, prepayment destroys the original capital structure, and the asset liability structure based on duration and convexity is no longer matched, resulting in risk exposure. Fourthly, when the market interest rate drops, the prepayment of mortgage loan makes the market value of bank assets have an upper limit.

As shown in Figure 1two curves represent the value-interest curve of mortgage: the solid line indicates non-prepayment and the dotted line indicates prepayment. When the contract stipulates that the mortgage loan cannot be paid in advance, the decrease of interest rate will cause the asset value of the bank to rise; however, when the interest rate falls to refers to the interest rate level that causes the borrower to prepay, that is, to exercise the embedded optionthe value of assets will encounter a bottleneck when the mortgage loan can be binary options strategy indicators in advance, and it will decrease gradually after reachingwhich will lead to the decrease of net assets of commercial banks.

Figure 1 The curve of relationship between market value of mortgage and interest rate. Analysis on the Option Characteristics of Housing Mortgage Loan For the option characteristics of prepayment of mortgage loans, the following is an example of Case 1.

Case 1. A borrower and a commercial bank sign a loan contract with a term of at zero time, in which the loan amount is unit 1, the penalty isand the lending rate is expressed by continuous compound interest rate.

When prepayment is not considered, the total borrowing cost is ; assuming that the benchmark interest rate changes to at time t, prepayment occurs, and the refinancing cost is ; ifthe rational borrower will prepay; otherwise, the prepayment will not be carried out. This method can be used for similar analysis whenever interest rate adjustment occurs.