Commercial mortgage prepayments under heterogeneous prepayment penalty structures

Journal of Real Estate Research, The, Jul-Sep 2003 by Fu, Qiang, LaCour-Little, Michael, Vandell, Kerry D

It has also been recognized that there is unobserved heterogeneity among borrowers. This heterogeneity is caused by the inability to identify all characteristics influencing prepayment behavior. Ignoring heterogeneity may bias parameter estimates. Unobserved heterogeneity is the source of "burnout" in prepayment modeling: two seemingly identical borrowers respond to identical prepayment incentive differently.

Modeling "burnout" has been a very difficult job in prepayment modeling. Traditionally, it has been modeled ex post through measuring borrower's past response (or failure in responding) to refinancing opportunities. Another type of burnout modeling explicitly assumes a distribution of prepayment response functions among groups of borrowers [see Hall (2000) for a review]. In industry models, this approach is in a form of "multi-population model" (e.g., Hayre, 1994; Hayre, Chaudhary and Young, 2000; or Patruno, 1994). A typical multi-population model assumes the borrowers belong to several populations (in practice, it is usually fewer than three populations for computational simplicity). Populations are assumed to have different refinancing sensitivities. As the borrowers are exposed to refinancing opportunities, the borrowers in the more refinancing sensitive groups prepay faster than the less sensitive groups and exit the population earlier, leaving the whole population with larger composition of "slower" refmancers. The overall refinancing sensitivities of the population is thus lowered. With several exceptions, academic research on this class of model has been rare. Stanton (1995) assumes a continuous distribution of transaction costs among all borrowers and calibrates the distribution on the observed data. The calibrated transaction costs, however, are unreasonably high (about 40%), which casts some doubt on an otherwise reasonable modeling approach. Deng, Quigley and Van Order (2000) assume 2-3 populations of borrowers in prepayment function. Deng and Quigley (2001) further extend the model in assuming a continuous distribution of borrower heterogeneity and incorporate a variable measuring a borrower's past failure in responding to refinancing opportunities into the distribution assumption of borrower heterogeneity. Both models show that unobserved heterogeneity exists and matters in prepayment modeling. The disadvantage of this multi/continuous population model, besides the great complexity involved, is that the choice of population is arbitrary, and there is no definitive evidence showing better performance relative to simpler approaches. Note that Ambrose and LaCour-Little (2000) employed the competing risk methodology controlling for unobserved heterogeneity and produced results qualitatively similar to simpler models without such controls. Accordingly, this study employs the simpler approach by simply including a measure of "burnout" equal to the cumulative sum of the past refinancing opportunities (constrained to zero during lockout period, if any).