# Probability and Mathematical Physics Seminar

#### Statistical analysis for rough volatility: Central limit theorems

**Speaker:**
Carsten Chong, Columbia University

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, April 7, 2023, 11:10 a.m.

**Synopsis:**

There is an intense debate in finance whether volatility in asset prices is rough or not. In non-finance language, this question can be rephrased as follows: Is it possible to determine the regularity of a process $\sigma_t$ if only its stochastic integral $\int_0^t \sigma_s dB_s$ can be observed? In this talk, I will show that the answer is “yes” and I will discuss a CLT result that can be used to construct an estimator with the best possible rate of convergence in a minimax sense. On the way, I will also explain how similar probabilistic tools can be used to solve statistical questions arising in turbulence physics and stochastic PDE 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).