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Importance sampling for option pricing with feedforward neural networks

Author

Listed:
  • Aleksandar Arandjelović

    (TU Wien)

  • Thorsten Rheinländer

    (TU Wien)

  • Pavel V. Shevchenko

    (Macquarie University)

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.

Suggested Citation

  • Aleksandar Arandjelović & Thorsten Rheinländer & Pavel V. Shevchenko, 2025. "Importance sampling for option pricing with feedforward neural networks," Finance and Stochastics, Springer, vol. 29(1), pages 97-141, January.
    • Handle: RePEc:spr:finsto:v:29:y:2025:i:1:d:10.1007_s00780-024-00549-x
    DOI: 10.1007/s00780-024-00549-x
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    Keywords

    Cameron–Martin space; Doléans–Dade exponential; Feedforward neural networks; Importance sampling; Universal approximation;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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