Importance sampling for option pricing with feedforward neural networks

Aleksandar Arandjelović (), Thorsten Rheinländer () and Pavel V. Shevchenko ()
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Aleksandar Arandjelović: TU Wien
Thorsten Rheinländer: TU Wien
Pavel V. Shevchenko: Macquarie University

Finance and Stochastics, 2025, vol. 29, issue 1, No 3, 97-141

Abstract: Abstract We study the problem of reducing the variance of Monte Carlo estimators through performing suitable changes of the sampling measure computed by feedforward neural networks. To this end, building on the concept of vector stochastic integration, we characterise the Cameron–Martin spaces of a large class of Gaussian measures induced by vector-valued continuous local martingales with deterministic covariation. We prove that feedforward neural networks enjoy, up to an isometry, the universal approximation property in these topological spaces. We then prove that sampling measures generated by feedforward neural networks can approximate the optimal sampling measure arbitrarily well. We conclude with a comprehensive numerical study pricing path-dependent European options for asset price models that incorporate factors such as changing business activity, knock-out barriers, dynamic correlations and high-dimensional baskets.

Keywords: Cameron–Martin space; Doléans–Dade exponential; Feedforward neural networks; Importance sampling; Universal approximation; 60G15; 65B99; 65C05; 68T07; 91G20; 91G60 (search for similar items in EconPapers)
JEL-codes: C15 C45 C63 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00780-024-00549-x

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