MBSの理論価格評価手法に関する基礎的研究 : 期限前償還オプション行使の金利経路依存性に注目して
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MBS (Mortgage Backed Securities) has been taken an interest in recent years in Japan. But the valuation is more difficult than all other bonds because of the uncertain cash flow in the future. The mortgagors hold the prepayment options to pay off their debt at any time, so the cash flow depends on the future path of the interest rate and so on. In, this study, I have attempted to value MBS theoretical price by following procedures applied the Monte Carlo simulation. Firstly, I have developed the prepayment model using the historical market data. The prepayment rate is determined by two factors in this model. One is the 6-month moving average of the deference between the mortgage rate and the 20 years forward interest rate that starts at 10 year. The other is the 1-year moving average of the ratio of the 20 years forward interest rate that starts at 10 year and 1 year forward interest rate that starts at 1 year. Secondly, I have developed the program to calculate MBS theoretical price. It generates numberless paths of the interest rate following the Wiener process, and calculates the prepayment rate using the above model. And it also calculates the yield of the MBS at the each path, let the average yield of all paths be the expected yield of MBS. These calculations have been repeated until then the expected yield agrees with the fair yield, MBS theoretical price is settled. As a result of this study, these procedures are expected to be useful as a handy method to value the theoretical price of MBS. But the appropriate fair yield is needed for the extremely precise valuation. To improve the precision of the valuation, the methods to value the effect of the Jiquidity to the yield will be required.
- 麗澤大学の論文
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