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.
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DOI : 10.1051/ps/2022008
Keywords: Stochastic differential equations, Greeks, integration by parts, Monte Carlo simulator
@article{PS_2022__26_1_304_0,
author = {Chen, Junchao and Frikha, Noufel and Li, Houzhi},
title = {Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift},
journal = {ESAIM: Probability and Statistics},
pages = {304--351},
year = {2022},
publisher = {EDP-Sciences},
volume = {26},
doi = {10.1051/ps/2022008},
mrnumber = {4467105},
zbl = {1492.60200},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2022008/}
}
TY - JOUR AU - Chen, Junchao AU - Frikha, Noufel AU - Li, Houzhi TI - Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift JO - ESAIM: Probability and Statistics PY - 2022 SP - 304 EP - 351 VL - 26 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ps/2022008/ DO - 10.1051/ps/2022008 LA - en ID - PS_2022__26_1_304_0 ER -
%0 Journal Article %A Chen, Junchao %A Frikha, Noufel %A Li, Houzhi %T Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift %J ESAIM: Probability and Statistics %D 2022 %P 304-351 %V 26 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ps/2022008/ %R 10.1051/ps/2022008 %G en %F PS_2022__26_1_304_0
Chen, Junchao; Frikha, Noufel; Li, Houzhi. Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift. ESAIM: Probability and Statistics, Tome 26 (2022), pp. 304-351. doi: 10.1051/ps/2022008
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