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On Copulas and their Application to CDO Pricing

by Benjamin Verschuere of the University of Toronto

January 2006

Abstract: In this paper we present a factor approach combined with copula functions to price tranches of synthetic Collateralized Debt Obligation (CDO) having totally inhomogeneous collateral (the obligors in the CDO pool have different spreads and different notional). While a CDO is a portfolio of defaultable fixed income products, copulas are functions which link univariate distributions together to build a multivariate distribution function. The attractiveness of copulas lies in their flexibility to simulate or fit dependant variables and their ability to provide scale invariant measures of association between random variables. When pricing a synthetic CDO, the copula function will be used in conjunction with the factor approach to model the obligors risk neutral joint default probabilities. This paper will, in one hand, interest people already familiar with the copula theory but unfamiliar to their application for the pricing of (correlation derivatives) financial instruments; while on the other hand, it will be relevant for people familiar with the credit derivatives products willing to know more about the copula functions.

Keywords: Copulas Function, Dependence Concept, Factor Modeling, Credit Derivatives, CDO.

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