Rational Prepayment and the Valuation of Mortgage-Backed Securities

Abstract

This article presents a new model of mortgage prepayments, based on rational decisions by mortgage holders. These mortgage bolders face beterogeneous transaction costs, which are explicitly modeled. The model is estimated using a version of Hansen's (1982) generalized method of moments, and is sbown to capture many of the empirical features of mortgage prepayment. Estimation results indicate that mortgage holders act as tbougb tbey face transaction costs tbat far exceed tbe explicit Costs usually incurred on refinancing. They also wait an average of more than a year before refinancing, even when it is optimal to do so. The model fits observed prepayment behavior as well as thee recent empirical model of Schwartz and Torous (1989). Implications for pricing mortgage-backed securities are' discussed A GNMA mortgage-backed security gives its owner a share in the cash flows from a pool of mortThis article is based on a chapter from my PhD. dissertation. I am grateful for helpful comments and suggestions to Oren Cheyette, Darrell Duffie, David Modest, Chester Span (the editor). Robert Whitelaw. Nicky King and an anonymous referee, as well as seminar participant.. at

Negative equity and foreclosure: Theory and evidence

“…However, the empirical literature has shown that, even when conditioning on observable mortgage characteristics and property characteristics, there is substantial heterogeneity in default behavior across borrowers. 23 A common explanation of this finding, advocated in the literature (see Stanton, 1995, for example), is that significant transactions costs are associated with defaulting, and these transactions costs differ across borrowers. As discussed above, these costs may include moving costs, default penalties that take the form of limited future access to credit markets, sentimental attachment to the home, or even the presence of moral qualms associated with defaulting on one's debts.…”

“…19 Stanton (1995) was the first study to incorporate transactions costs into a model of mortgage termination. 20 Kau, Keenan, and Kim (1994) make this point in the context of an option-theoretic model.…”

“…We find that approximately 100,300 Massachusetts borrowers were in a position of negative equity in 1991:Q4. 8 Of these borrowers, approximately 6.4 percent (slightly fewer than 6,500 borrowers) ended up in foreclosure over the next three years. This percentage may seem extremely low to many readers, but in Section 3 below, we show that it is consistent with economic theory.…”

“…This should provide very good coverage of borrowers with negative equity in 1991:Q4, as high house price appreciation in the mid-to-late 1980s meant that borrowers who purchased their homes before 1987 were very unlikely to be in a negative equity position at the end of 1991. 8 We are able to calculate initial LTV ratios, and thus equity positions for 277,470 Massachusetts borrowers in the fourth quarter of 1991. This number is much smaller than the active number of mortgage borrowers during this time period, because we do not have data on purchase deeds before January 1, 1987.…”

Computing the endogenous mortgage rate without iterations

“…They require about 10% of decrease on their monthly mortgage payments (if we compute these "savings" implied by 1% mortgage rate decrease) to refinance and they do not prepay for exogenous reasons. This specification is somewhat similar to the specification of the prepayment in [10], where the prepayment rate, however, was assumed to be governed by the borrower's liability (the so called option-based approach).…”