A Gaussian Process Based Method with Deep Kernel Learning for Pricing High-Dimensional American Options

Jirong Zhuang (), Deng Ding (), Weiguo Lu (), Xuan Wu () and Gangnan Yuan ()
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Jirong Zhuang: University of Macau
Deng Ding: University of Macau
Weiguo Lu: University of Macau
Xuan Wu: University of Macau
Gangnan Yuan: Great Bay Institute for Advanced Study

Computational Economics, 2025, vol. 66, issue 5, No 4, 3687-3708

Abstract: Abstract In this work, we present a novel machine learning approach for pricing high-dimensional American options based on the modified Gaussian process regression (GPR). We incorporate deep kernel learning and sparse variational Gaussian processes to address the challenges traditionally associated with GPR. These challenges include its diminished reliability in high-dimensional scenarios and the excessive computational costs associated with processing extensive numbers of simulated paths. Our findings indicate that the proposed method surpasses the performance of the least squares Monte Carlo method in high-dimensional scenarios, particularly when the underlying assets are modeled by Merton’s jump diffusion model. Moreover, our approach does not exhibit a significant increase in computational time as the number of dimensions grows. Consequently, this method emerges as a potential tool for alleviating the challenges posed by the curse of dimensionality.

Keywords: Deep kernel learning; Gaussian process; High-dimensional american option; Machine learning; Regression based monte carlo method (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10614-024-10833-9

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