Volume 26, 2022
Fractional Dynamics in Natural Phenomena
|Page(s)||304 - 351|
|Published online||12 August 2022|
Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift
Université de Paris, Laboratoire de Probabilités, Statistique et Modélisation (LPSM), 75013 Paris, France
* Corresponding author: email@example.com
Accepted: 7 July 2022
In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation technique for Markov semigroups, our formulae are based on a simple Markov chain evolving on a random time grid for which we develop a tailor-made Malliavin calculus. Among other applications, an unbiased Monte Carlo path simulation method stems from our formulas so that it can be used in order to numerically compute with optimal complexity option prices as well as their sensitivities with respect to the initial values or Greeks in finance, namely the Delta and Vega, for a large class of non-smooth European payoff. Numerical results are proposed to illustrate the efficiency of the method.
Mathematics Subject Classification: 60H20 / 60H07 / 60H30 / 65C05 / 65C30
Key words: Stochastic differential equations / Greeks / integration by parts / Monte Carlo simulator
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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