A Stochastic U.S. House Price Model for Valuing Residential Mortgages and Other House Price–Dependent Assets

Abstract

House prices are an important input to default and prepayment models used to project residential mortgage cash flows. I present a stochastic model of U.S. house prices to be used in valuing residential mortgages and other house price–dependent assets. The model generates a forecast of the full distribution of future house prices over long time horizons. The fundamental value of house prices is modeled as a function of rental rates and interest rates. House prices move relative to fundamental value based on serial correlation and mean-reversion dynamics. A 1,000-path Monte Carlo simulation of future house prices results in a positively sloped term structure of the expected volatility of house prices as of December 31, 2011. This slope flattens over certain horizons because of mean-reversion dynamics but steepens again because of the relation between house prices and interest rates. The model accounts for the changing relation between house prices and interest rates, and the importance of this relation in measuring the interest rate risk of mortgages is demonstrated.