Extreme Asymmetric Volatility: VIX and S&P 500
Résumé
Asymmetric volatility in equity markets has been widely documented in finance (Bekaert and Wu (2000)). We study asymmetric volatility for daily S&P 500 index returns and VIX index changes, thereby examining the relation between extreme changes in risk-neutral volatility expectations and in aggregate asset prices. To this aim, we model market returns, implied VIX market volatility and volatility of VIX volatility, showing that volatility of volatility is asymmetric in that past positive volatility shocks drive positive shocks to volatility of volatility. Our results document the existence of a significant extreme asymmetric volatility effect, i.e. there is contemporaneous volatility-return tail dependence for crashes but not for booms. We then outline aggregate market price implications of extreme asymmetric volatility, indicating, for example, that a one-in-a-hundred trading day innovation to average VIX volatility under volatility feedback relates to an expected market drop of more than 4 percent.