基于仿真利率路径和Spread-Prepaymet曲线的MBS定价方法

Pricing Method for MBS Based on Simulated Interest Rate Paths and Spread-prepayment Curve

房产抵押贷款证券的定价与市场利率的路径密切相关。以市场现行利率期限结构为基准,用蒙特卡罗方法生成利率路径,为房产抵押贷款证券定价。为克服传统的Vasicek、CIR等利率模型的弱点,引进利率水平因素的均值回归项和斜率因素的均值回归项,以产生平稳的利率路径。模型中的波动率由互换市场的报价计算得出,以反映市场的对未来的预期。根据利差与提前还本速度间的函数关系,由历史数据统计得到"利差-提前支付速度曲线",作为提前还本模型。最后对比了各种模型生成的利率路径,以及参数选取对MBS价格的影响。

Pricing of Mortgage-backed securities, MBS, depends on the path of the market interest rate. Taking the prevailing interest rate term structure as benchmark, an approach was discussed for MBS pricing, based on the interest rate paths generated in the method of Monte Carlo. To conquer the weakness of traditional Vasicek and CIR models, the differential equation of interest rate was modified by a level mean reversion term and a slope mean reversion term, with stable and feasible interest rate paths generated Market quoted price of swap was used to estimate implied volatility surface in simulation model. In the consideration that the refinance speed was decided by the spread of MBS rate and prevailing loan rate, a spread-prepayment speed curve estimated from history data was used to measure prepayment. At the last, properties of interest paths generated by different model were compared and influence ofpararneter was discussed.