以蒙地卡羅模擬法評價房貸轉付證券

Pricing Mortgage Pass-through Securities by Simulation

余秉霖(Ping-Lin Yu)

指導教授 ： 洪茂蔚

國立臺灣大學/管理學院/國際企業學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.00195

摘要

在評價房貸轉付證券時必須先對其標的資產(一籃子的房貸)進行評價，因為轉付證券持有人的現金流量是由該群房貸戶所決定。房貸契約所內含的選擇權與不同房貸戶的行為使得房貸轉付證券具有提前執行與路徑相依的性質。本文選擇以Longstaff and Schwartz (2001)所提出的最小平方模擬法(Least Squares Monte Carlo method , LSM)來評價具有此類性質的證券；該模擬法對轉付證券的評價流程與McConnell and Singh (1994)所提出的觀念相似，卻能減少其所需的步驟，而原來的單因子模型在此則延伸至兩因子模型，同時考慮提前還款與違約風險。最後我們提供評價結果與敏感性分析來檢驗模型的有效性與穩定性。

關鍵字

蒙地卡羅模擬法 ； 房貸轉付證券

並列摘要

When valuing a mortgage pass-through security, one must go back to the valuation of its underlying asset, a pool of risky mortgages, since it is mortgage borrowers who decide the timing of cash flows received by securities holders. Embedded options in mortgage contracts and mortgage borrowers’ suboptimal behavior make pass-through securities American-style and path-dependent. In this study, we use the Least Squares Monte Carlo method (LSM) proposed by Longstaff and Schwartz (2001) to value pass-through securities with such features. Incidentally, employing LSM reduces McConnell and Singh’s (1994) two-step framework into a one-step model. Furthermore, the model is extended to a two-factor model, in which both prepayment and default are considered so that pass-through securities and mortgage insurance can be priced at the same time. Finally, we provide not only our valuation results but several sensitivity analyses to determine the robustness of our algorithm.

並列關鍵字

mortgage pass-through security ； Monte Carlo Simulation

參考文獻

Boyle, P. P., 1979, “Options: A Monte Carlo Approach“, Journal of Financial Economics, 4, 323-338.

Brennan, M. J., and E. S. Schwartz, 1985, “Determinants of GNMA Mortgage Prices,” AREUEA Journal, 13, 3, 209–28.

Broadie, M., and P. Glasserman, 1997, “Pricing American-style Securities Using Simualation,” Journal of Economic Dynamics and Control, 21, 8-9, 1323-1352.

Calhoun, C. A., and Y. Deng, 2002, “A Dynamic Analysis of Fixed-and Adjustable-Rate Mortgage Terminations,” Journal of Real Estate Finance and Economics, 24, 9-33

Cox, J., S. Ross, M. and Rubinstein 1979, "Option Pricing: A Simplified Approach", Journal of Financial Economics, September, 229-263.