Estimating the Hurst parameter from the zero vanna implied volatility and its dual

Abstract

The covariance between the return of an asset and its realized volatility can be approxi- mated as the difference between two specific implied volatilities. In this paper it is proved that in the small time-to-maturity limit the approximation error tends to zero. In addition a direct relation between the short time-to-maturity covariance and slope of the at-the-money implied volatility is established. The limit theorems are valid for stochastic volatility models with Hurst parameter H \in (0,1). An application of the results is to accurately approximate the Hurst parameter using only a discrete set of implied volatilities. Numerical examples under the rough Bergomi model are presented.

This paper is available at https://arxiv.org/abs/2510.26310