Copula functions: A semi-parametric approach to the pricing of basket credit derivatives

Abstract

The aim of this thesis is to present the copula function theory. Copulafunctions are useful to analyze the dependence between financial stochasticvariables, and in particular, these methods allow the pricing of basket creditderivatives. We will first introduce the basic mathematical concepts relatedto copula functions. Then, we will show that they are very powerful tools inorder to model the dependence structure of a random sample. Indeed, thecopula function family is a very large family and each copula function depictsa certain kind of dependence structure. As a consequence, a copula functioncan be chosen to accurately fit empirical data.The second step of our study will be the pricing of credit derivatives. Todo so, we will perform a Monte-Carlo simulation on a basket CDS. The defaultcorrelation structure will be represented by different copula models.