Default correlation is an important piece of information for risk management of credit portfolios because portfolio managers must accurately estimate portfolio losses that depend on joint default events between obligors in a portfolio. Das, Fong and Geng (2001) find that default rates of debts in credit portfolios are significantly correlated and estimates of credit losses are substantially different if default correlation is ignored.
The recent subprime mortgage crisis is an acute example that underscores the importance of understanding default correlation. Cowan and Cowan (2004) show that default correlations between subprime loans are substantially higher than those between commercial bonds and loans, and that default correlation increases as the rating of the lender declines. High default correlations among loans compound the current problem in the subprime mortgage market.
Though default correlation is important for risk management and credit analysis, this information is often unavailable because default correlation cannot be measured directly. In particular, it is difficult to uncover default correlation based on observed default data for high-grade bonds because default is a rare event. A number of models have been developed to estimate default risk and to explore the structure of default correlation. Majority of these models adopt either the structural or reduced-form approach.
The reduced-form approach models default as an intensity process that is determined by exogenously state variables (see, among others, Jarrow and Turnbull, 1995; Madam and Unal, 1998; Duffie and Singleton, 1999; and Das, Duffie, Kapadia, and Saita, 2007). This approach allows the default intensity process to be directly estimated from the credit risk premium without relying on parameters related to the firm's underlying unobserved asset value. Because of this advantage, the reduced-form approach has been widely used to explain credit spreads (see Duffie and Singleton, 1999). Notwithstanding this advantage, formulation of default intensity as an exogenous factor limits the application of the reduced-form model to prediction of default correlation between firms.
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Inferring Default Correlation from Equity Return Correlation
