Roughness of the Implied Volatility

TL;DR

This paper investigates the roughness of implied volatility and the VIX index, proposing they may serve as better proxies for the true underlying volatility compared to realized volatility measures, which can be biased.

Contribution

It introduces a method to measure the roughness of implied volatility and evaluates its effectiveness as a proxy for actual volatility, addressing biases in high-frequency data analysis.

Findings

Implied volatility exhibits roughness consistent with theoretical models

VIX index roughness correlates with implied volatility measures

Implied volatility may be a more accurate proxy for true 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.