Title: Is volatility rough
Authors: Tetsuya Takabatake - Osaka university (Japan) [presenting]
Masaaki Fukasawa - Osaka university (Japan)
Rebecca Westphal - ETH Zurich (Switzerland)
Abstract: In recent years, the rough volatility model, which is a kind of stochastic volatility models whose log-volatility process is driven by a fractional Brownian motion with the very small Hurst parameter, attracts much attention in the community of Mathematical Finance because the rough volatility model can reproduce many stylized facts in financial markets. From statistical point of view, the previous studies are, however, not satisfactory in several aspects. Among others, we would like to emphasize that there is no estimator for the roughness of volatility whose consistency is proven so far. We propose a quasi-likelihood estimator for the Hurst and diffusion parameters of the fractional Brownian motion driving the volatility process based on high frequently observed realized volatility data, and prove its consistency under high frequency asymptotics. Moreover, we examine the finite sample performance of our estimator by simulations, and apply our estimator to empirical analysis by using the realized volatility data provided by the Oxford-Man realized library. Our data analysis suggests that the volatility is indeed rough; actually it is much rougher than considered in previous studies.