Pricing Mortgage-Backed Securities – First Hitting Time Approach

Abstract

This paper develops a pricing model and derives a closed-form formula for valuing mortgage-backed securities (MBSs) that embed a barrier option feature while the optimal prepayment or refinancing choices of borrowers are endogenously determined. Given that “real estate investors” tend to prepay a loan relentlessly, an MBS with a high concentration of investor borrowers implies a lower MBS value. We specify the prepayment behavior of borrowers by using the first hitting time as a proxy for the trigger point of prepayment when house prices or interest rates hit a pre-determined barrier. Our results show that the MBS value is positively related to loan to value and house price volatility while negatively related to the proportion of real estate investors and interest rate volatility. We also find evidence which shows that the MBS value may increase due to the effects of the “longevity” of mortgages, which outweigh the effects of default or prepayment as house price volatility increases. This model provides a faster pricing tool of MBSs than Monte Carlo simulation while retaining higher model accuracy and consistency than the hazard model approach.

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Keywords

Mortgage-Backed Security, First Hitting Time, Prepayment, Default

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