Woodhead Behavior and the Pricing of Residential Mortgages

Option theory which has dominated residential mortgage prepayment and default research implies that a borrower will exercise prepayment or default options if the call option or put option, respectively, is "in the money" by some optimal amount. Empirical research provides evidence that the financial value of the call option is strongly associated with exercise of the prepayment option, and the probability that the put option is in the money is strongly associated with exercise of the default option. Nevertheless, evidence also shows that in general borrowers do not behave as "ruthlessly" as the theory predicts. This paper investigates the irrational behavior of those borrowers who do not call their mortgages even when the option is deeply into the money. We develop an option-based empirical model of prepayment and default in a competing risks hazard framework to analyze this phenomenon -- the behavior of irrational "wood-heads." Of course we do not observe "woodheads" explicitly in any body of data. Instead, we analyze the heterogeneity and correlates of unobserved heterogeneity within a large sample of mortgage holders. We utilize recent simulation techniques in a three-stage estimation approach to estimate a competing risks hazard model of mortgage prepayment and default with unobserved heterogeneity which is due in part to the behavior of "woodheads." We then analyze the impact of this behavior on the market value of mortgage and mortgage-backed securities using the industry-standard Monte Carlo simulation pricing approach. The results indicate the empirical importance of heterogeneity and non optimizing behavior in the valuation and pricing of mortgages.