Housing price dynamics and the valuation of mortgage default options

The mortgage pricing literature typically assumes that house prices evolve according to a geometric Brownian motion; the literature then employs conventional arbitrage arguments to value mortgages and their imbedded default options. However, this is not a realistic approach to the modeling of the real estate market. In this paper, we propose a method of polynomial approximation to value the mortgage default option. This methodology does not rely on arbitrage arguments. Rather than assuming the house price to be a random walk process, we set up a more realistic house price model with three return components and then use actual transaction data in four cities to estimate the price process. We then apply the empirically estimated house price model to value the default option. We show that variation in the forecastable returns can produce significant variation in the mortgage default option price. The serial correlation of the market return is found to have strong impacts on the price of the default option in all four cities. The random walk model is not able to use the information of current market return and persistent idiosyncratic error for the valuation of the mortgage default option, and therefore may lead to mispricing of the option. (C) 1996 Academic Press, Inc.