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Variance Reduction Applied to Machine Learning for Pricing Bermudan/American Options in High Dimension

Author

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  • Ludovic Gouden`ege
  • Andrea Molent
  • Antonino Zanette

Abstract

In this paper we propose an efficient method to compute the price of multi-asset American options, based on Machine Learning, Monte Carlo simulations and variance reduction technique. Specifically, the options we consider are written on a basket of assets, each of them following a Black-Scholes dynamics. In the wake of Ludkovski's approach (2018), we implement here a backward dynamic programming algorithm which considers a finite number of uniformly distributed exercise dates. On these dates, the option value is computed as the maximum between the exercise value and the continuation value, which is obtained by means of Gaussian process regression technique and Monte Carlo simulations. Such a method performs well for low dimension baskets but it is not accurate for very high dimension baskets. In order to improve the dimension range, we employ the European option price as a control variate, which allows us to treat very large baskets and moreover to reduce the variance of price estimators. Numerical tests show that the proposed algorithm is fast and reliable, and it can handle also American options on very large baskets of assets, overcoming the problem of the curse of dimensionality.

Suggested Citation

  • Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2019. "Variance Reduction Applied to Machine Learning for Pricing Bermudan/American Options in High Dimension," Papers 1903.11275, arXiv.org, revised Dec 2019.
    • Handle: RePEc:arx:papers:1903.11275
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    References listed on IDEAS

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    Cited by:

    1. Zineb El Filali Ech-Chafiq & Pierre Henry-Labordere & Jérôme Lelong, 2021. "Pricing Bermudan options using regression trees/random forests," Working Papers hal-03436046, HAL.
    2. Zineb El Filali Ech-Chafiq & Pierre Henry Labordère & Jérôme Lelong, 2023. "Pricing Bermudan options using regression trees/random forests," Post-Print hal-03436046, HAL.
    3. Zineb El Filali Ech-Chafiq & Pierre Henry-Labordere & J'er^ome Lelong, 2021. "Pricing Bermudan options using regression trees/random forests," Papers 2201.02587, arXiv.org, revised Jun 2023.
    4. Bernard Lapeyre & Jérôme Lelong, 2021. "Neural network regression for Bermudan option pricing," Post-Print hal-02183587, HAL.
    5. Stefan Kremsner & Alexander Steinicke & Michaela Szolgyenyi, 2020. "A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics," Papers 2010.15757, arXiv.org, revised Dec 2020.
    6. Lu Xiong & Jiyao Luo & Hanna Vise & Madison White, 2023. "Distributed Least-Squares Monte Carlo for American Option Pricing," Risks, MDPI, vol. 11(8), pages 1-16, August.
    7. Stefan Kremsner & Alexander Steinicke & Michaela Szölgyenyi, 2020. "A Deep Neural Network Algorithm for Semilinear Elliptic PDEs with Applications in Insurance Mathematics," Risks, MDPI, vol. 8(4), pages 1-18, December.
    8. Riccardo Aiolfi & Nicola Moreni & Marco Bianchetti & Marco Scaringi & Filippo Fogliani, 2021. "Learning Bermudans," Papers 2105.00655, arXiv.org.
    9. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.

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