Correlation between default and recovery has an important bearing on credit risk capital. Here, Rahul Sen shows that the effect can be modelled efficiently by allowing multiple loss states in the Vasicek framework. Heavy-tailed distributions result for arbitrary loss data, and simple non-parametric capital formulas apply for both large and granular portfolios
The credit component of the Basel economic capital framework is based on Vasicek's portfolio loss model (see Vasicek (2002) and Schonbucher (2000)). This is a two-state model: at the end of a given period, an obligor is placed in either a non-defaulted state or a defaulted state characterised by a fixed loss severity. Vasicek employs a Gaussian copula framework with a single common factor, the economy, accounting for correlation among obligors. As the economy varies, the portfolio default rate varies, but the loss given default (LGD) is held constant at some value Lavg regardless of the state of the economy. Typically, Lavg is set to the expected LGD (ELGD), an unconditional average over all economic states.
There is strong empirical evidence, however, that default and recovery rates both vary with the economy. Frye and others (see Frye (2005) and references therein) have argued that the constant LGD assumption is a potentially serious weakness of the Basel framework. Frye shows that coupling between default rates and LGD is pervasive across industry and debt type. To capture the higher loss rates that accompany adverse economic conditions, he suggests replacing the ELGD by a semi-empirical function of it. Another empirical suggestion is to use a 'downturn LGD', corresponding to an economic downturn. This has been criticised on the grounds that different types of portfolios respond to economic downturns with different lags (RMA Capital Working Group (2005)).
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