Sensitivities via rough paths

Abstract

Motivated by a problematic coming from mathematical finance, the paper deals with existing and additional results on the continuity and the differentiability of the Itô map associated to rough differential equations. These regularity results together with the Malliavin calculus are applied to the sensitivities analysis of stochastic differential equations driven by multidimensional Gaussian processes with continuous paths as the fractional Brownian motion. The well-known results on greeks in the Itô stochastic calculus framework are extended to stochastic differential equations driven by a Gaussian process which is not a semi-martingale.