Credit migration and derivatives pricing using copulas

The multivariate modelling of default risk is a crucial aspect of the pricing of credit derivative products referencing a portfolio of underlying assets, and the evaluation of Value at Risk of such portfolios. This paper proposes a model for the joint dynamic behavior of credit ratings for several …rms. Namely, individual credit ratings are modelled by univariate continuous time Markov chain, while their joint dynamics is modelled using copulas. A by-product of the method is the joint laws of the default times of all the …rms in the portfolio. The use of copulas allows us to incorporate our knowledge of the modelling of univariate processes, into a multivariate framework. The Normal and Student copulas commonly used in the literature as well as by practitioners do not produce very di¤erent estimates of default risk prices. We show that this result is restricted to these two two basic copulas. That is, for any other family of copula, the choice of the copula greatly a¤ects the pricing of default risk. Key Words: Copula, Markov chain, credit risk, credit rating migration J.E.L. classi…cation: G10, G20, G28, C16 Send correspondence to Nicolas Papageorgiou,Finance Department, HEC Montréal, 3000 Cote Sainte-Catherine, Montreal QC H3T 2A7, Canada. or at [email protected] . All the authors are at HEC Montréal can be reached at www.hec.ca/pages/…rstname.lastname. Funding in partial support of this work was provided by the Natural Sciences and Engineering Research Council of Canada, the Fonds québécois de la recherche sur la nature et les technologies, and the Institut de …nance mathématique de Montréal. We thank Hyung-Seob Kim for his help in creating the database.