On the volatility of volatility

More than you might want to know about volatility of the S&P500 index in this research article I've written with my PhD student Brian Murray. Brian has completed his dissertation work here (four research articles on dark energy, instabilities, black holes, etc.) and has decided he wants to pursue a career as a quant. Anyone interested in hiring a sharp young problem solver, please let me know. Previous posts on volatility.

My favorite footnote from the article:
"Implied volatility which is systematically larger than realized volatility would seem to provide a risk-free arbitrage, since it means all options contracts are overpriced. In an idealized world of log-normal price fluctuations, a trader could sell options contracts and hedge away the risk by holding cash and the underlying. However, in the real world, where volatility is itself volatile, there is no foolproof way to completely hedge away the risk of selling an option. An option seller is paid a premium to bear this risk, namely the systematic difference between implied and realized volatilities."


Title: On the volatility of volatility

Abstract: The Chicago Board Options Exchange (CBOE) Volatility Index, VIX, is calculated based on prices of out-of-the-money put and call options on the S&P 500 index (SPX). Sometimes called the "investor fear gauge,'' the VIX is a measure of the implied volatility of the SPX, and is observed to be correlated with the 30-day realized volatility of the SPX. Changes in the VIX are observed to be negatively correlated with changes in the SPX. However, no significant correlation between changes in the VIX and changes in the 30-day realized volatility of the SPX are observed. We investigate whether this indicates a mispricing of options following large VIX moves, and examine the relation to excess returns from variance swaps.