Volume 19, 2015
|Page(s)||515 - 543|
|Published online||16 November 2015|
Sensitivities via rough paths
Laboratoire ISTI, ESME Sudria, 51 Boulevard de Brandebourg, 94200 Ivry-sur-Seine, France
Received: 11 April 2014
Revised: 9 October 2014
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.
Mathematics Subject Classification: 60H10
Key words: Rough paths / Rough differential equations / Malliavin calculus / sensitivities / mathematical finance / Gaussian processes
© EDP Sciences, SMAI, 2015
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