Sensitivities via Rough Paths

TL;DR

This paper investigates the regularity of the Itô map in rough differential equations and applies these results, along with Malliavin calculus, to sensitivities analysis of stochastic differential equations driven by Gaussian processes, with applications in finance.

Contribution

It introduces new regularity results for the Itô map in rough differential equations and extends Greeks computation for SDEs driven by Gaussian processes, including fractional Brownian motion.

Findings

Enhanced methods for sensitivities analysis in stochastic models

Extended Greeks computation to fractional Brownian motion

Validated approaches with financial applications and simulations

Abstract

Motivated by a problematic coming from mathematical finance, this paper is devoted to existing and additional results of continuity and differentiability of the It\^o map associated to rough differential equations. These regularity results together with Malliavin calculus are applied to sensitivities analysis for stochastic differential equations driven by multidimensional Gaussian processes with continuous paths, especially fractional Brownian motions. Precisely, in that framework, results on computation of greeks for It\^o's stochastic differential equations are extended. An application in mathematical finance, and simulations, are provided.