| Summary: | 碩士 === 國立臺灣大學 === 財務金融學研究所 === 99 === This paper talks about the reverse mortgage program in the United States called Home Equity Conversion Mortgage (HECM). We come up with a method for calculating the repayment the lenders can get, and further find out that the repayment will be influenced by the stochastic interest rate model. Since the HECM is a non-recourse debt. When the loan terminates, if the property value is sufficient to pay the outstanding loan balance, the remaining value usually flows to the borrower or his/her beneficiaries. If the proceed is not enough to cover the loan balance, the non-recourse provision prevents the lender from pursuing other assets belonging to the borrower. So the repayment will be influenced by three major risks. The first one is the longevity risk, and the second one is the house price risk, and the final one is the interest rate risk. In conventional way of computing the repayment, the earlier method will discount the future cash flows by using long-term mean of interest rate. In this paper, we derive a new method for computing the repayment by using Fourier Transform under Vasicek and CIR model. We discover that the repayment will be different from the results by conventional way, and we further discover that if the house price and the interest rate have correlation, we also have interest rate model risk when computing the repayment.
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