Hedging the black swan: Conditional heteroskedasticity and tail dependence in S&P500 and VIX

Abstract

The recent financial crisis has accentuated the fact that extreme outcomes have been overlooked and not dealt with adequately. While extreme value theories have existed for a long time, the multivariate variant is difficult to handle in the financial markets due to the prevalent heteroskedasticity embedded in most financial time series, and the complex extremal dependence that cannot be conveniently captured by a single structure. Moreover, most of the existing approaches are based on a limiting argument in which all variables become large at the same rate. In this paper, we show how the conditional approach of Heffernan and Tawn (2004) can be implemented to model extremal dependence between financial time series. We use a hedging example based on VIX futures to demonstrate the flexibility and superiority of the conditional approach against the conventional OLS regression approach.