it would be beneficial to address the timing of the default event, as do roll rate models, and to account for static predictive variables, as do scoring and life-of-loan loss models. However, a mortgage default model also must allow for prepayment and other options, as do roll rate and option-based models, as well as incorporate time-varying predictive variables (i.e., current loan-to-value or asset-to-liability ratios) as do option-based models.

Hazard Models
The Hazard model is a modeling technique that addresses many of the concerns raised above. Moreover, hazard models are heavily used in prepayment modeling (Davidson et. al. (2003), Hayre (2001), etc.). As a result, though the technique is less commonly applied to default, its usage in the prepayment modeling area makes it well-understood by investors on Wall Street. In fact, the valuation and market risk measurement of MBS, ABS, CLO, CDO, etc. most commonly depend upon hazard models of prepayments.

There is an enormous amount of academic and regulatory literature that applies hazard models to both prepayments and defaults. For example, Alexander et. al. (2002) examines subprime mortgage performance; Calem and LaCour-Little (2002) is the foundation for the current Basel II regulations for mortgages; and OFEHO (2002) explains the application of hazard models to mortgages in the context of capital regulation for Fannie Mae and Freddie Mac.

Why are Default and Prepayment "Competing" Risks?
Since the hazard technique is well-understood on Wall Street and in academia, one might expect that a default model for mortgages could simply be estimated and then used with an existing prepayment model. As it turns out, however, prepayments and defaults are "competing risks" that require simultaneous development and estimation of models.

Consider the fact that two hazards, such as prepayments and defaults, may not be statistically related, but the outcomes may be related in other ways. For each hazard, the probability of transition over longer time intervals will depend on transition probabilities of the other hazard. For example, the lifetime default probability for a mortgage may be lower if monthly prepayment probabilities are higher.

Moreover, some observed predictive variables, such as the current loan-to-value (LTV) ratio or the FICO score, might affect both the hazard of prepayment and the hazard of default. Clearly, increased current LTVs or decreased FICOs likely increase defaults for mortgages; however, the same variables may decrease prepayment likelihood. Separating out the effects of these predictive variables on both hazards simultaneously is best handled by a modeling technique known as "competing risk" hazard models. >>>