Pricing Multiname Credit Derivatives: Heavy Tailed Hybrid Approach

by Roy Mashal  of the Columbia Business School, and
Marco Naldi of Lehman Brothers, Inc.

January 7, 2002

Abstract:  In recent years, credit derivatives have become the main tool for transferring and hedging credit risk. The credit derivatives market has grown rapidly both in volume and in the breadth of the instruments it offers. Among the most complicated of these instruments are the multiname ones. These are instruments with payoffs that are contingent on the default realization in a portfolio of names. The modeling of dependent defaults is difficult because there is very little historical data available about joint defaults and because the prices of those instruments are not quoted. Therefore the models cannot be calibrated, neither to defaults nor to prices.

In this paper, we present a methodology for estimation, simulation, and pricing of multiname contingent instruments. Our model is a hybrid of the well-known structural and reduced form approaches for modeling defaults. The dependence structure of our model is of a t-copula that possesses non-trivial tail dependence. The t-copula allows for more joint extreme events, which have a big impact on the prices of miltiname instruments, e.g. n^th-to-default baskets and CDOs. We demonstrate this impact with n^th-to-default baskets.

JEL Classification: G13.

Keywords: Credit risk, credit derivatives, copula functions, portfolio models.

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