Ebook The Empirical Relation between Credit Quality, Recoveries, and Correlation in a Simple Credit Risk Model
The current US-subprime mortgage crisis highlights that during economic downturns, likelihood and severity of multiple borrowers may deteriorate jointly. This is a particular concern in today’s credit markets where via mechanisms such as collateralized debt obligations, credit portfolios rather than single name credits are exposed to losses within contractual boundaries. According to a recent study by the British Bankers’ Association (2006), 54 percent of the global $20 trillion credit derivatives market consists of portfolio products. The evaluation of these requires the understanding of individual risk drivers as well as their dependence structure. Simplifying assumptions in existing models often lead to an underestimation of risks, particularly during economic downturns.
For instance, credit portfolio models aggregate parameters for the likelihood, severity and dependence structure underlying a credit portfolio and forecast the distribution of future credit losses. It is common practice to model these parameters independently and to introduce the dependence structure thereafter. Different contributions try to incorporate the dependence structure between the default events (compare e.g., Lucas 1995, Dietsch & Petey 2004, Hamerle et al. 2006, Frey & McNeil 2002, 2003, Rösch & Scheule 2004, Rösch 2005, McNeil & Wendin 2007) and between the default events and related recoveries (compare e.g., Frye 2000, Pykhtin 2003, Tasche 2004, Düllmann & Trapp 2005, Rösch & Scheule 2005).
Examples for well known credit portfolio models are Credit Risk (Credit Suisse Financial Products 1997), Credit Metrics (Gupton et al. 1997) and Credit Portfolio Manager (Gupton et al. 1997). Newer applications in relation to collateralized debt obligations are VECTOR from Fitch rating agency (see Fitch Ratings 2006), CDOROM from Moody’s rating agency (see Moody’s 2006) and CDO Evaluator from Standard and Poor’s rating agency (see Standard & Poor’s 2005).
The literature on the estimation of severity parameters such as recoveries or losses given default includes a limited number of contributions (compare e.g., Carey 1998, Altman et al. 2006, Cantor & Varma 2005, Schuermann 2005, Acharya et al. 2007). Unfortunately, these contributions rely on the estimation of unconditional OLS regression models and do not take into account that recoveries can only be observed when a default event occurs. Three exceptions are Altman et al. (2001), Pykhtin (2003), and Hamerle et al. (2007). Altman et al. (2001) show the relation between default probability and expected recovery rate in a Merton model approach and the sensitivity w.r.t asset volatility.
Thereby their model accounts for the fact that recoveries are only observable if a default occurs. Pykhtin (2003) also accounts for this mortality bias and derives closed-form expressions for the Expected Loss and the Value-at-Risk. However, these papers do not provide empirical solutions for parameter estimation. Pykhtin (2003) even acknowledges that ”[The average LGD] is impossible to estimate”. Hamerle et al. (2007) show by simulation that the estimates of isolated recovery models are biased but do not provide an analytical justification for that. Furthermore, their model is based on two systematic risk factors and thus does not allow a simple analytical solution for the Value-at-Risk in an asymptotic portfolio as for instance in Basel II, see Gordy (2003).
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