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Inaccurate Dependence Measures in Credit Models for Non-Normal Variables
Abstract
Due to the assumption of normally distributed variables, conventional credit models have been criticized for not being able to identify possible extreme losses. As an alternative, some methods have incorporated non-normal variables in the estimation of the probability of default in loan portfolios and credit derivatives. One of the objectives of these methods is to express heavy tails of the distributions (which tends to better represent the reality of the credit market since economic and financial variables typically present more extreme occurrences than indicated by the normal distribution). However, as this paper shows, the derivation of some of these alternative models does not comply with all the assumptions implicit in the formula used to develop the models and this mistake results in misleading dependence measures. Our theoretical arguments are supported by simulations which show that, in terms of the calculation of regulatory capital for financial institutions, models for non-normal variables overestimate losses and this bias is substantial for high levels of confidence (up to 13 times higher than the losses observed in the simulated credit portfolio). We present some ideas to start solving this problem although the estimation of the dependence parameter is still an open question.
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