Neural variance reduction for stochastic differential equations

Hinds, P.D.; Tretyakov, M.V.

Abstract

Variance reduction techniques are of crucial importance for the efficiency of Monte Carlo simulations in finance applications. We propose the use of neural SDEs, with control variates parameterized by neural networks, in order to learn approximately optimal control variates and hence reduce variance as trajectories of the SDEs are being simulated. We consider SDEs driven by Brownian motion and, more generally, by L´evy processes including those with infinite activity. For the latter case, we prove optimality conditions for the variance reduction. Several numerical examples from option pricing are presented.

Citation

Hinds, P., & Tretyakov, M. (2023). Neural variance reduction for stochastic differential equations. Journal of Computational Finance, 27(3), 1-41. https://doi.org/10.21314/JCF.2023.010

• Journal Article Type: Article
• Acceptance Date: Sep 4, 2023
• Online Publication Date: Nov 29, 2023
• Publication Date: 2023-12
• Deposit Date: Sep 22, 2023
• Journal: Journal of Computational Finance
• Print ISSN: 1460-1559
• Electronic ISSN: 1755-2850
• Publisher: Incisive Media
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 3
• Pages: 1-41
• DOI: https://doi.org/10.21314/JCF.2023.010
• Public URL: https://nottingham-repository.worktribe.com/output/25367490
• Publisher URL: https://www.risk.net/journal-of-computational-finance/7958436/neural-variance-reduction-for-stochastic-differential-equations