Roughness of the Implied Volatility

Abstract

The measures of roughness of the volatility in the litterature are based on the realized volatility of high frequency data. Some authors show that this leads to a biased estimate, and does not necessarily indicate roughness of the underlying volatility process. Here, we attempt to measure the roughness of the implied volatility of short term options, as well as of the VIX index, and evaluate whether they may be more appropriate proxies of the underlying instant volatility.