Woodhead Behavior and the Pricing of Residential Mortgages
Mortgage terminations arise because borrowers exercise options. This paper investigates the 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 â€œwoodheads.â€ Of course we do not observe â€œwoodheadsâ€ explicitly in any body of data. Instead, we analyze the 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 is due in part to the behavior of â€œwoodheads.â€ 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 by 0.7 to 2 percent 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.
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