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Credit Risk Assessment via Copulas: Association Invariance and Risk Neutrality

by Elisa Luciano of the University of Turin & ICER

July 12, 2005

Abstract: Copula functions have proven to be extremely useful in describing joint default and survival probabilities. We overview the state of the art and point out some modelling issues, such as the choice of a specific copula and of the amount of dependence, as well as re-mapping of models or dependence invariance. We also discuss how to simplify credit models using factors. The survey leads us to focus on historical versus risk neutral dependence. We present an original methodology for inferring risk neutral dependence from vulnerable credit derivatives, provide an application to market data and explore its impact on the fees of some credit derivatives. The choice of the appropriate copula turns out to be crucial, and to effect derivative prices more than the switch from historical to risk neutral measures.

JEL Classification: G12.

Keywords: default dependence, copula functions, credit derivative pricing, vulnerable credit derivatives.

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