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Extreme Events and Multi-Name Credit Derivatives

by Roy Mashal of Lehman Brothers Inc.,
Marco Naldi of Lehman Brothers Inc., and
Assaf Zeevi of Columbia University

September 9, 2003

Abstract: The dependence structure of asset returns lies at the heart of a class of models that is widely employed for the valuation of multi-name credit derivatives. In this work, we study the dependence structure of asset returns using copula functions. In particular, using a statistical methodology that relies on a minimal amount of distributional assumptions, we compare the dependence structures of asset and equity returns to provide some insight into the common practice of estimating the former using equity data. Our results show that the presence of joint extreme events in the data is not compatible with the assumption of Normal dependence, and support the use of equity returns as proxies for asset returns. Furthermore, we present evidence that the likelihood of joint extreme events does not diminish as we decrease the sampling frequency of our observations. Building on our empirical findings, we then describe how to capture the effects of joint extreme events by means of a simple and computationally efficient time-to-default simulation. Using a t-copula model, we analyze the impact of extreme events on the fair values and risk measures of popular multi-name credit derivatives such as nth-to-default baskets and synthetic loss tranches.

Keywords: copulas, dependence structure, credit derivatives.

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