Learning parameter dependence for Fourier-based option pricing with tensor trains
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915445074821120 |
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| author | Sakurai, Rihito Takahashi, Haruto Miyamoto, Koichi |
| author_facet | Sakurai, Rihito Takahashi, Haruto Miyamoto, Koichi |
| contents | A long-standing issue in mathematical finance is the speed-up of option pricing, especially for multi-asset options. A recent study has proposed to use tensor train learning algorithms to speed up Fourier transform (FT)-based option pricing, utilizing the ability of tensor trains to compress high-dimensional tensors. Another usage of the tensor train is to compress functions, including their parameter dependence. Here, we propose a pricing method, where, by a tensor train learning algorithm, we build tensor trains that approximate functions appearing in FT-based option pricing with their parameter dependence and efficiently calculate the option price for the varying input parameters. As a benchmark test, we run the proposed method to price a multi-asset option for the various values of volatilities and present asset prices. We show that, in the tested cases involving up to 11 assets, the proposed method outperforms Monte Carlo-based option pricing with $10^6$ paths in terms of computational complexity while keeping better accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00701 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning parameter dependence for Fourier-based option pricing with tensor trains Sakurai, Rihito Takahashi, Haruto Miyamoto, Koichi Computational Finance Quantum Physics A long-standing issue in mathematical finance is the speed-up of option pricing, especially for multi-asset options. A recent study has proposed to use tensor train learning algorithms to speed up Fourier transform (FT)-based option pricing, utilizing the ability of tensor trains to compress high-dimensional tensors. Another usage of the tensor train is to compress functions, including their parameter dependence. Here, we propose a pricing method, where, by a tensor train learning algorithm, we build tensor trains that approximate functions appearing in FT-based option pricing with their parameter dependence and efficiently calculate the option price for the varying input parameters. As a benchmark test, we run the proposed method to price a multi-asset option for the various values of volatilities and present asset prices. We show that, in the tested cases involving up to 11 assets, the proposed method outperforms Monte Carlo-based option pricing with $10^6$ paths in terms of computational complexity while keeping better accuracy. |
| title | Learning parameter dependence for Fourier-based option pricing with tensor trains |
| topic | Computational Finance Quantum Physics |
| url | https://arxiv.org/abs/2405.00701 |