Extreme events and multi-name credit derivatives

Roy Mashal, Marco Naldi and Assaf Zeevi

The dependence structure of asset returns lies at the heart of a class of models widely employed for the valuation of multi-name credit derivatives as we saw in the last chapter. In this chapter, we study the dependence structure of asset returns using copula functions. Employing a statistical methodology that relies on a minimal amount of distributional assumptions, we first investigate whether the popular tenet of Normal dependence between asset returns is supported on the basis of empirical observations. We also 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 incompatible 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