@MISC{Huang14volatility-of-volatilityrisk, author = {Darien Huang and Ivan Shaliastovich}, title = {Volatility-of-Volatility Risk}, year = {2014} }

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Abstract

We show that time-varying volatility-of-volatility is a separate and significant risk factor that affects prices and risk premia in options markets. Shocks to volatility-of-volatility command a negative price of risk, which is an additional source of risk distinct from volatility risk. We use the VVIX index, which is a model-free, forward-looking measure of the volatility-of-volatility constructed from VIX options, as an ex-ante measure of expected volatility-of-volatility risk. Using high-frequency data, we shed light on the fine structure of variance risks and document that while the VVIX is a strong predictor of future realized volatility-of-volatility, the VIX itself is not. Options that pay off when volatility-of-volatility is high have significantly negative returns. In the cross-section, options more sensitive to volatility-of-volatility risks earn more negative expected returns. In the time-series, high expectations of future volatility-of-volatility predicts more negative expected returns to delta-hedged option portfolios. The VVIX explains fluctuations in the risk premia in both the S&P500 and VIX options markets. Our results are robust to the presence of jump risks. Overall, the evidence we find supports a significant negative risk premium for time-varying volatility-of-volatility risk.