住房抵押贷款定价模型与数值分析

A Numerical Approach to the Valuation of Residential Mortgage Loans

期权的价值取决于借款人的违约行为和提前偿还行为,而借款人的违约行为和提前偿还行为又取决于当前的利率水平和房屋价格。CIR模型表明,住房抵押贷款合同的价值满足一个偏微分方程。运用交替方向隐性有限差分法对住房抵押贷款合同的价值进行数值分析的结果表明,由于提前偿还期权和违约期权的存在,贷款合同的价值远远小于贷款总额。房屋价格的波动幅度与抵押贷款合同的价值负相关,而利率波动幅度与抵押贷款合同的价值正相关。为减少商业银行面临的提前偿还风险和违约风险,住房抵押贷款合同需要使用浮动利率贷款,同时还应加快发展我国住房抵押贷款保险市场。

The value of options to prepay or to default depends upon the borrowers＇ default and prepayment behaviours. Since prepayment involves consideration of the term structure of interest rates, while default is concerned with the house price they are chosen as the underlying source of uncertainty. This paper presents a numerical procedure to solve the partial difference equation that must be satisfied by the value of a mortgage loan according to CIR model. The Alternating Direction Implicit （ADI） scheme is illustrated to solve the partial difference equation numerically. The numerical results show that the joint option value is considerably high. The sensitivity analysis indicates that house price volatility and interest rate volatility varies inversely with the mortgage value to the borrower.