Automatic control variates for option pricing using neural networks

El Filali Ech-Chafiq Zineb (), Lelong Jérôme () and Reghai Adil ()
Additional contact information
El Filali Ech-Chafiq Zineb: Université Grenoble Alpes, CNRS, Grenoble INP, LJK, 38000Grenoble; and Quantitative Analyst at Natixis, Paris, France
Lelong Jérôme: Université Grenoble Alpes, CNRS, Grenoble INP, LJK, 38000Grenoble, France
Reghai Adil: Head of Quantitative Research, Equity and Commodity Markets, Natixis, 47 quai d’Austerlitz, 75013Paris, France

Monte Carlo Methods and Applications, 2021, vol. 27, issue 2, 91-104

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 σM{\frac{\sigma}{\sqrt{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. 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.

Keywords: Monte Carlo; neural networks; variance reduction; control variate; effective dimension (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/mcma-2020-2081 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

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:bpj:mcmeap:v:27:y:2021:i:2:p:91-104:n:7

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/mcma/html

DOI: 10.1515/mcma-2020-2081

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().