Abstract
While option-theoretic models are widely used in valuation of other fixed-income instruments, their applications for the valuation of mortgage-backed securities face challenges. Mortgages are explicitly written with a call option, which allows mortgagors to prepay their mortgages any time before the maturity. The magnitude and timing of exercising the prepayment options are not purely driven by economic factors, but also the mortgagor’s individual preferences and personal behaviours. This brings difficulties to valuing mortgage-backed securities with conventional models. In this thesis we aim to explore the prepayment risk caused uncertainties in valuation of mortgage-backed securities. We start with empirically examining an option-theoretic model proposed by Kalotay, Yang and Fabozzi (2004). This model has special features to treat borrower heterogeneity and suboptimal exercises of the prepayment options. Based on the empirical results, we propose to employ linear prepayment functions to model borrower heterogeneity. The new MBS valuation model with the integration of linear prepayment functions is also tested with empirical data. Our results suggest that mortgages with different coupon rates have different refinancing tendencies even towards the same market rate change. Therefore, assuming the same refinancing pattern to all classes of mortgages may lead to errors in pricing mortgages and MBSs. For mortgages with coupon rate below the prevailing refinancing rate (as proxied by the 30 year libor rate) plus the refinancing cost, a prepayment function with a low initial prepayment rate and a high slope will model the prepayments best. On the other hand, for mortgages with coupon rate above the current refinancing rate plus the refinancing cost, a prepayment function with a high initial prepayment and a mild slope will perform best. Meanwhile, refinancing burnout is also an important factor in modelling mortgage prepayment. Our results suggest that when the underlying mortgages are seasoned mortgages, especially when the prepayment option has been deep-in-the-money for a long time, the low initial prepayment high slope function will model their prepayments the best. Once these different refinancing tendencies are factored in the modelling of mortgage prepayment, the accuracy of the MBS valuation model is greatly improved.