Volatility of volatility and tail risk premiums

This paper reports on tail risk premiums in two tail risk hedging strategies: the S&P 500 puts and the VIX calls. As a new measure of tail risk, we suggest using a model-free, risk-neutral measure of the volatility of volatility implied by a cross section of the VIX options, which we call the VVIX index. The tail risk measured by the VVIX index has forecasting power for future tail risk hedge returns. Specifically, consistent with the literature on rare disasters, an increase in the VVIX index raises the current prices of tail risk hedges and thus lowers their subsequent returns over the next three to four weeks. Furthermore, we find that volatility of volatility risk and its associated risk premium both significantly contribute to the forecasting power of the VVIX index, and that the predictability largely results from the integrated volatility of volatility rather than volatility jumps.