:Speaker: Prof. Mathieu Rosenbaum, Université Pierre et Marie Curie (Paris VI) and École Polytechnique

Title: The microscopic foundations of volatility statistical properties

Abstract: In this talk, we will first review a series of statistical stylized facts of the volatility

process typically encountered in financial data. We will in particular focus on the rough

nature of the volatility, its persistence properties, and on the so-called leverage effect.

In the second part of the talk, we will show how such features can be explained from

a microscopic point of view. More precisely, we will introduce specific point processes

(Hawkes processes) enabling us to model accurately the agents behaviour on financial

markets at the high frequency scale. Then we will demonstrate that the volatility arising

from the long term dynamics of such point processes enjoys the properties detailed in

the first part of the talk. This presentation is based on joint works with Omar El Euch, Jim Gatheral and Thibault Jaisson.