Valuing Prepayment and Default in a Fixed‐Rate Mortgage: A Bivariate Binomial Options Pricing Technique

Abstract

This paper uses a bivariate binomial options pricing technique to value prepayment and default options in a fixed-rate mortgage. By forcing the two underlying state variables (real-estate value and spot rate of interest) to undergo transformations, a computationally simple bivariate binomial lattice is created. Compared with the finite-difference model of Kau et al. (1992, 1994), large option value differences (over 5% of the loan) are rare and occur when there is a downward-sloping term structure and slow adjustment. The smallest option value differences (less than 0.5% of the loan) tend to occur when interest-rate volatility and real estate volatility are low.

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