Prepayment and the Valuation of Mortgage‐Backed Securities

Abstract

This paper puts forward a valuation framework for mortgage‐backed securities. Rather than imposing an optimal, value‐minimizing call condition, we assume that at each point in time there exists a probability of prepaying; this conditional probability depends upon the prevailing state of the economy. To implement our valuation procedure, we use maximum‐likelihood techniques to estimate a prepayment function in light of recent aggregate GNMA prepayment experience. By integrating this empirical prepayment function into our valuation framework, we provide a complete model to value mortgage‐backed securities.

Rational Prepayment and the Valuation of Mortgage-Backed Securities

“…of the pool will be relatively high. To model this behavior, previous empirical papers often assume that a mortgage's prepayment probability depends explicitly on the total prepayment of the pool to date [see, for example, Schwartz and Torous (1989)]. The problem with using such an endogenous state variable is that it is unclear what sort of behavior would lead to the specific burnout representations used.…”

“…The model produces prepayment behavior that matches closely that actually observed. Measured in terms of percentage of variance explained, this model fits the data better than the recent empirical prepayment model of Schwartz and Torous (1989). The estimated transaction costs can be explained as a way of capturing unmodeled credit imperfections of mortgage holders.…”

“…If the interest rate process were to change, or there were some change to mortgage contract terms, mortgage prepayment behavior would also change. Purely empirical models, including that of Schwartz and Torous (1989), can make no predictions about the magnitude of this change.…”

“…1 To value and hedge these securities requires a model of mortgage prepayment behavior, since this determines the timing of the cash flows. Schwartz and Torous (1989) is a recent example of a large body of literature, both academic and institutional, that empirically models prepayment as a function of some set of (nonmodel based) explanatory variables. Most such models use either past prepayment tates or some other endogenous variable, such as burnout, 2 to "explain" current prepayment.…”

Numerical Valuation of High Dimensional Multivariate European Securities

“…It has then been used by several authors for the valuation of path dependent contingent claims. In particular, the method has been used for pricing mortgage-backed securities (see Schwartz and Torous (1989), Hutchinson and Zenios (1991)). Barraquand (1993) presents the method of Quadratic Resampling for Monte Carlo valuation of European securities with many underlying assets.…”