Copulas - pricing credit derivatives

Abstract

Credit derivatives are derivative instruments whose pay out is linked to the credit worthiness of an underlying obligor. Credit derivatives are increasingly becoming popular as risk mitigation instruments. This paper presents a methodology to price nth to default basket credit derivative swaps. Copulas have been used in the pricing. Copulas are a way to construct joint probability distribution and to generate dependence between two or more random variables. Copulas are a more powerful tool than correlation to characterize the dependence between two variables due to their properties of tail dependence, transformation neutrality and ability to capture non-linear dependence. Specifically, t copula, Gaussian copula and Gumbel copula have been used in our methodology. The methodology adopted for pricing involves using the market quotes for CDS of individual assets in the basket to calibrate the default probability function of each asset. In addition, we have included in the pricing model, the risk of the CDS writer defaulting before the maturity of the CDS contract. Copulas have been used for this purpose also. Keywords: Copula, basket credit derivative, nth to default, counter party risk, copula estimation