[Pricing d'option financière avec volatilité stochastique par une métode mixte EDP / Monte-Carlo]
We propose a pricing method for derivatives modeled by a set of stochastic differential equations with the objective of reducing the computing time. The speed up observed in our numerical implementation can be as large as 50. The method is based on a joint use of Monte-Carlo simulations and PDE or analytical formulas. The method is tested in the framework of the Heston stochastic volatility model with and without barriers.
Nous proposons dans cette note une méthode pour accélérer les calculs d'options financières modélis'ees par un système d'équations différentielles stochastiques. La méthode consiste à intégrer un groupe d'équation par une méthode de Monte-Carlo et les autres par une méthode déterministe, EDP ou formules de Black–Scholes. La méthode est présentée avec une justification euristique seulement sur le modl‘ele de Heston puis testée numériquement et comparée à une solution Monte-Carlo classique du modlèle de Heston. Les simulations numériques montrent qu'on peut obtenir un facteur d'accérération allant jusqu'a 50.
Accepté le :
Publié le :
Grégoire Loeper 1, 2 ; Olivier Pironneau 2
@article{CRMATH_2009__347_9-10_559_0,
author = {Gr\'egoire Loeper and Olivier Pironneau},
title = {A mixed {PDE/Monte-Carlo} method for stochastic volatility models},
journal = {Comptes Rendus. Math\'ematique},
pages = {559--563},
publisher = {Elsevier},
volume = {347},
number = {9-10},
year = {2009},
doi = {10.1016/j.crma.2009.02.021},
language = {en},
}
Grégoire Loeper; Olivier Pironneau. A mixed PDE/Monte-Carlo method for stochastic volatility models. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 559-563. doi : 10.1016/j.crma.2009.02.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.02.021/
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