Models of corporate default fall into two broad categories, structural models and reduced form models. Structural models consider the evolution of the value of the firm, with default assumed to occur if firm value should fall below some insolvency threshold. Structural models have the practical advantage of being able to make use of the firm's current stock price.
Stock returns are very sensitive to all kinds of information about a firm's financial condition, and they are available daily, unlike accounting statements. But structural models also have serious drawbacks, including the need to take proper account of the firm's capital structure, which may be quite complex, and the difficulty in modeling important non-default credit events, such as a ratings downgrade.
Reduced form models, which are the focus of this paper, treat default as a random event that has a positive probability of occurrence for any firm at any time. In the basic reduced form model, a credit event corresponds to the first jump time of a Poisson process with a constant hazard rate. An "event" can be defined flexibly, to be default, downgrade or upgrade from one bond rating category to another, or any other welldefined change of state.
The resulting model yields a Markov chain for the occurrence of credit events. The reduced form approach is widely used for credit risk analysis in both academic and real world research, e.g., Jarrow, Lando and Turnbull (1995) and (1997), Lando and Skodeberg (2002), Duffie et al (2005), and Koopman et al (2005).