Joint defaults in a non-normal world: empirical estimations and suggestions for Basel Accords based on copulas

Abstract

Credit risk models widely used in the financial market nowadays assume that losses are normally distributed and have linear dependence. Nevertheless it is well known that asset returns (loans included) are not normally distributed and present tail dependence. Therefore the traditional approaches are not able to capture possible stronger association among higher losses and tend to underestimate the probability of joint extreme losses. Copula functions are an alternative to overcome this drawback since they yield accurate dependence measures regardless of the distribution of the variables analysed. This technique was first applied to credit risk in 2000 but the studies in this field have been concentrated on corporate debt and derivatives. We filled this gap in the literature by employing copulas to estimate the dependence among consumer loans. In an empirical study based on a credit card portfolio of a large UK bank, we found evidence that standard models are misspecified as the dependence across default rates in the dataset is seldom expressed by the (Gaussian) copula implicit in those models. The comparison between estimations of joint high default rates from the conventional approach and from the best-fit copulas confirmed the superiority of the latter method. The initial investigation concerning pairs of credit segments was extended to groups of three segments with the purpose of accounting for potential heterogeneous dependence within the portfolio. To do so, we introduced vine copulas (combinations of bivariate copulas to form high-dimension copulas) to credit risk and the empirical estimations of simultaneous excessive defaults based on this technique were better than both the estimations from the pairwise copulas and from the conventional models. Another contribution of this work concerns the application of copulas to a method derived from the limited credit models: the calculation of the capital required to cover unexpected losses in financial institutions. Two models were proposed and, according to simulations, outperformed the current method (Basel) in most of the scenarios considered.