The Pricing of Default-Free Mortgages

Abstract

In this paper we examine the household's option to prepay or call a standard fixed-rate mortgage.Results based on simulation indicate that the value of this option is sensitive to the expected path of interest rates, the variation around that path, risk aversion and refinancing costs.Unfortunately, efforts to estimate the interest rate process (by us and by previous authors) have met with only limited success, and uncertainty exists regarding the degree of risk aversion and the magnitude of refinancing costs.Thus we conclude that the application of contingent-claims methodology to options on bonds is conceptually more difficult and operationally less reliable than is the analogous application to options on stocks.Despite these reservations concerning the use of our model as a technique for absolute valuation, preliminary findings on the effects of changes in mortgage contract design on the value of the prepayment option are encouraging.For example, our estimate of the relative values of the call options on 30-and 15-year mortgages and on level-payment and graduated-payment mortgages appear to be reasonably robust with respect to specifications of the interest rate process and the other parameters.These findings suggest that our model may be of considerable use within the context of relative or comparative valuation.

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