The Grouped t-Copula with an Application to Credit Risk

Abstract

We describe a model that takes into account the tail dependence present in a large set of historical risk factor data using the modern concept of copulas. We extend the popular t-copula to obtain a new grouped t-copula which describes more accurately the dependence among risk factors of different classes. We explain how to estimate the parameters of the grouped t-copula and apply the method to a problem in credit risk management with a large number of risk factors. We measure the downside risk over one month for an internationally diversified credit portfolio and we observe that the new model gives different results to the t-copula and seems better able to capture the risk in a large set of risk factors.