Copula Functions and their Application in Pricing and Risk Managing Multiname Credit Derivative Products

by Stefano S. Galiani of King's College London

September 4, 2003

Abstract: This paper presents and numerically implements a methodology to price credit derivative products referencing a portfolio of underlying assets. We develop a copula based framework to model the default dependency among obligors and offer algorithms for pricing Basket Default Swaps and Collateralized Debt Obligations. A risk neutral methodology by which [we] calibrate copula parameters to market quotes is taken into account, and different methods of calibration are illustrated and implemented. We numerically calculate the sensitivity of prices to the main state variables affecting their values, namely recovery rates, default correlation and credit quality of the underlying portfolio. By assuming two alternative specifications (Gaussian and Student's t) of the copula function used to describe the joint distribution of default times among obligors, we then demonstrate the effect of the asymptotic tail dependence on modeling portfolio defaults and losses.

Keywords: Basket default swap, Collateralized debt obligation, Credit default swap, Copula functions, Maximum likelihood, Tail dependence, Default times, Simulation algorithm, Hazard rates, Loss distribution.

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