Credit Portfolio Risk and Diversification
The present financial crisis illustrates in a dramatic fashion that a deeper understanding of portfolio credit risk is needed. While defaults are rare events, the ensuing losses can be substantial and have a serious impact on the entire financial sector and the economy as a whole. We can distinguish two conceptually different approaches to credit risk modeling: structural and reduced-form approaches. The structural models go back to Black and Scholes (1973) and Merton (1974). The Merton model assumes that a company has a certain amount of zero-coupon debt which becomes due at a fixed maturity date. The market value of the company is modeled by a stochastic process. A possible default and the associated recovery rate are determined directly from this market value at maturity. In the reduced-form approach default probabilities and recovery rates are described independently by stochastic models. These models aim to reproduce the dependence of these quantities on common covariates or risk factors. For some well known examples of reduced-form models see, e.g., Jarrow and Turnbull (1995), Jarrow et al. (1997), Duffie and Singleton (1999), Hull and White (2000) and Schönbucher (2003). First passage models were first introduced by Black and Cox (1976) and constitute a mixed approach. As in the Merton model, the ...