Woodhead Behavior and the Pricing of Residential Mortgages

Abstract

Mortgage terminations arise because borrowers exercise options. This paper investigates the non-optimal and apparently irrational behavior of those borrowers who do not terminate their mortgages even when the exercise value of the option is deeply in the money. We develop an option-based empirical model to analyze this phenomenon -- the behavior of irrational or boundedly rational “woodheads.” Of course we do not observe “woodheads” explicitly in any body of data. Instead, we analyze correlates of unobserved heterogeneity within a large sample of mortgage holders. We develop a three-stage maximum likelihood (3SML) estimator using martingale transforms to estimate the competing risks of mortgage prepayment and default, recognizing unobserved heterogeneity which in part generates the behavior of “woodheads.” The extended model is clearly superior to alternatives on statistical grounds. We then analyze the economic implications of this more powerful model. We analyze the predictions of the model for the valuation and pricing of mortgage pools and mortgage-backed securities. Based upon an extensive Monte Carlo simulation, we find that the 3SML model yields prices for seasoned mortgage pools that deviate quite substantially from more primitive estimates. The results indicate the empirical importance of heterogeneity and the implications of non-optimizing behavior for the valuation and pricing of mortgages and mortgage-backed securities.