Seminar by Carsten Chong

Please Note: This seminar will be given in person.

Statistical Inference for Rough Volatility: Central Limit Theorems Seminar

In recent years, there has been substantive empirical evidence that stochastic volatility is rough. In other words, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter H<0.5. In this paper, we derive a consistent and asymptotically mixed normal estimator of H based on high-frequency price observations. In contrast to previous works, we work in a semiparametric setting and do not assume any a priori relationship between volatility estimators and true volatility. Furthermore, our estimator attains a rate of convergence that is known to be optimal in a minimax sense in parametric rough volatility models.

This talk is based on joint work with Marc Hoffmann (Paris Dauphine), Yanghui Liu (Baruch College), Mathieu Rosenbaum and Grégoire Szymanski (both Ecole Polytechnique).