Department seminar by Mikko Pakkanen

Please Note: This seminar will be given online.

Rough volatility – Re-examining empirical evidence through the lens of generalised method of moments

In late 2014, Jim Gatheral, Thibault Jaisson and Mathieu Rosenbaum released the first preprint of their ground-breaking paper "Volatility is rough", arguing that financial market volatility should be modelled by stochastic processes with rough trajectories, such as a fractional Brownian motion with Hurst index below 0.5. While Gatheral, Jaisson and Rosenbaum's empirical findings on the roughness of realised volatility have since been replicated across different asset classes and with thousands of assets, determining the roughness of realised volatility remains a delicate statistical problem. It is complicated by the fact that we can only observe volatility as a time integral (integrated variance) with measurement error (estimated by means of realised variance). Integration is a smoothening operation while measurement error increases the perceived roughness of the measurements, giving rise to two counteracting sources of bias whose net effect is unclear. In particular, critics have questioned to what degree roughness of volatility can be distinguished from measurement error. In this talk, I will present a novel generalised method of moments (GMM) estimation technique for general log-normal volatility models, aiming to address this concern. The GMM estimator accommodates both the impact of integration and the presence of measurement error, the latter through a bias correction. After presenting asymptotic theory for the GMM estimator, I will demonstrate by Monte Carlo experiments that the bias correction is indispensable. Indeed, without it, non-rough volatility may be estimated as rough, but once it is incorporated, the bias problem is, for all practical purposes, resolved. Finally, by applying the GMM estimator to empirical realised volatility data on 29 stock market indices worldwide, I show that Gatheral, Jaisson and Rosenbaum's conclusion stands: realised volatility is indeed best described by a rough process.

Based on joint work with Anine Bolko, Kim Christensen and Bezirgen Veliyev.