Martin Hillebrand proposes a portfolio credit risk model with dependent loss given default (LGD), offering a reasonable economic interpretation that is easily applicable to real data. He builds a precise mathematical framework, and stresses some important issues to consider when modelling dependent LGD Most credit risk models assume loss given default (LGD) is a constant proportion of any credit loss, and ignore the fact that LGD is itself an important driver of portfolio credit risk because of its possible dependence on economic cycles. The Basel Committee on Banking Supervision (2004) acknowledged this importance by starting a discussion with the banking industry aimed at investigating this issue. Empirical evidence for dependent LGD is provided by data presented in Altman et al (2003) and Moody's (2003). Approaches to modelling dependent LGD have been suggested during the past five years, but none of these seem to have had an impact on present practice. In fact, it is very hard to obtain a model that has a reasonable economic interpretation, can be calibrated by available data, and is based on a proper statistical setting. In particular, a proper statistical model should incorporate the observation that expected LGD and default probability (PD) are, conditional on the economic cycle, dependent but not comonotonous. Hence, a stochastic dependence and not a deterministic functional relation should be modelled. In this article, we discuss the up-to-date proposed models in this context, and suggest a new model that addresses these issues. We start with a homogeneous portfolio of m credits, for simplicity each with exposure one. We are interested in the loss L of the portfolio within one year. A statistician's approach would be to take past losses of this portfolio, and calculate quantities, which allow for risk assessment and prediction. To estimate value-at-risk, methods from extreme value theory can be applied to estimate quantiles outside the range of observations. Such purely data- and simulation-driven methods, however, require a certain data sample size that has not been available for LGD yet. Also, one might miss important economic mechanisms, which influence future losses, and may not yet be visible in past data. - Click to download pdf...
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