MBS valuation and prepayments

Abstract

This paper not only provides a comparison of recent models in the valuation of mortgage-backed securities but also proposes an integrated model that addresses important issues of path-dependence, exogenous prepayment, transaction costs, mortgagors’ heterogeneity, and the housing devaluation effect.

Recent research can be categorized into two frameworks: empirical and theoretical option pricing. Purely empirically derived models often consider estimation of the prepayment model and pricing of the mortgage-backed security as distinct problems, and thus preclude explanation and prediction for the price behavior of the security. Some earlier theoretical models regard mortgage-backed securities as default-free callable bonds, prohibiting the mortgagors from exercising the default (put) option, and therefore induce bias on the pricing of mortgage-backed securities. Other earlier models assume homogeneity of mortgagors and consequently fail to address important issues of premium burnout effect and the path-dependence problem.

The model proposed is a two-factor model in which the housing price process is incorporated to account for the effect of mortgagor’s default and to capture the impact of housing devaluation. Default is correctly modeled in terms of its actual payoff through a guarantee to the investors of the security such that the discrepancy is eliminated by assuming mortgage securities as either default-free or unin-sured. Housing prices have been rising at unsustainable rates nation wide, especially along the coasts, suggesting a possible substantial weakening in house appreciation at some point in the future. The effect of housing devaluation is specifically modeled by considering the possibility that the mortgagor might be restrained from prepayment even if interest rates make it advantageous to refinance.

Mortgagors’ heterogeneity and the separation of exogenous and endogenous prepayments are explicitly handled in the model. Heterogeneity is incorporated by introducing heterogeneous refinancing transaction costs. The inclusion of heterogeneous transaction costs not only captures premium burnout effect but also solves the path-dependence problem. Finally, the model separates exogenous prepayment from endogenous prepayment, and estimates their distinct magnitudes from observed prepayment data. This construction provides a better understanding for these two important components of prepayment behavior. The generalized method of moments is proposed and can be employed to produce appropriate parameter estimates.