  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.

Mathematical Finance