Automatic Control Variates for Option Pricing using Neural Networks

Jérôme Lelong (), Zineb El Filali Ech-Chafiq () and Adil Reghai
Additional contact information
Jérôme Lelong: DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes
Zineb El Filali Ech-Chafiq: Natixis Asset Management, DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes
Adil Reghai: Natixis Asset Management

Post-Print from HAL

Abstract: Many pricing problems boil down to the computation of a high dimensional integral, which is usually estimated using Monte Carlo. In fact, the accuracy of a Monte Carlo estimator with M simulations is given by σ √ M. Meaning that its convergence is immune to the dimension of the problem. However, this convergence can be relatively slow depending on the variance σ of the function to be integrated. To resolve such a problem, one would perform some variance reduction techniques such as importance sampling, stratification, or control variates. In this paper, we will study two approaches for improving the convergence of Monte Carlo using Neural Networks. The first approach relies on the fact that many high dimensional financial problems are of low effective dimensions[15]. We expose a method to reduce the dimension of such problems in order to keep only the necessary variables. The integration can then be done using fast numerical integration techniques such as Gaussian quadrature. The second approach consists in building an automatic control variate using neural networks. We learn the function to be integrated (which incorporates the diffusion model plus the payoff function) in order to build a network that is highly correlated to it. As the network that we use can be integrated exactly, we can use it as a control variate.

Date: 2021
New Economics Papers: this item is included in nep-cmp and nep-cwa
Note: View the original document on HAL open archive server: https://hal.univ-grenoble-alpes.fr/hal-02891798v1
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Monte Carlo Methods and Applications, 2021, 27 (2), pp.91-104. ⟨10.1515/mcma-2020-2081⟩

Downloads: (external link)
https://hal.univ-grenoble-alpes.fr/hal-02891798v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02891798

DOI: 10.1515/mcma-2020-2081

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().