École Nationale Supérieure de
Techniques Avancées

Abstract

This work aims to understand several aspects of the roughness of volatility recently universally observed on financial assets in the "rough" regime with a Hurst index H < 1/2. We are interested particularly in simulating volatility, implying a fractionnaire brownian motion, more precisely in analysing the weak error hoping to have a clear link between it and the discretization step. First of all, we use an exact simulation method, that of Cholesky, thus an approximate method using the hybrid scheme for the semi-stationary Brownian motions introduced by Bennedsen, Lunde et Pakkanen, then an improved version of this scheme. Finally we draw from the numerical observations obtained a relation linking the weak error and the step of discretization.