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

This paper uses a bivariate binomial options pricing technique to value the prepayment and default options in a fixed-rate mortgage. The American style options are dependent on two stochastic variables: (1) house price, (2) one year spot rate. The paper uses the standard lognormal process for house price and the CIR square-root process for interest rates. By forcing the two underlying state variables to undergo transformations, two new uncorrelated variables with constant volatilities are established. With constant volatilities, a computationally simple bivariate binomial tree is formed which greatly reduces the complexity of working with two state variables and is pedagogicallyuseful. Using this procedure, the price of any real estate contingent claim whose value is dependent on the one year spot rate and house price can be determined. Results are compared with those from a finite difference model