A Gaussian Process Based Method with Deep Kernel Learning for Pricing High-dimensional American Options
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913319429865472 |
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| author | Zhuang, Jirong Ding, Deng Lu, Weiguo Wu, Xuan Yuan, Gangnan |
| author_facet | Zhuang, Jirong Ding, Deng Lu, Weiguo Wu, Xuan Yuan, Gangnan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07211 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Gaussian Process Based Method with Deep Kernel Learning for Pricing High-dimensional American Options Zhuang, Jirong Ding, Deng Lu, Weiguo Wu, Xuan Yuan, Gangnan Computational Finance 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. |
| title | A Gaussian Process Based Method with Deep Kernel Learning for Pricing High-dimensional American Options |
| topic | Computational Finance |
| url | https://arxiv.org/abs/2311.07211 |