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Pricing Swap Credit Risk with Copulas

by Umberto Cherubini of the University of Bologna

January 6, 2004

Abstract: We apply copula functions to evaluate counterpart risk in swap transactions. Using copulas allows to generalise the approach proposed by Sorensen and Bollier (1994), allowing for dependence between swap rates and counterparty default. Counterpart risk is represented by a sequence of vulnerable swaptions, which are priced using Cherubini and Luciano (2002) approach. Using copulas grants maximum flexibility with the choice of term structure and default risk models, as well as with the specification of the dependence structure between interest rate and credit risk. Closed form hedging and pricing formulas are derived for extreme dependence cases and for copula functions of the Fréchet family. An empirical application based on actual market data has shown that dependence affects both the level and the slope credit spreads, particularly for the case in which a credit institution is paying fixed. The effect is reversed in the case in which the financial institution pays floating.

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