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Learning parameter dependence for Fourier-based option pricing with tensor trains

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  • Rihito Sakurai
  • Haruto Takahashi
  • Koichi Miyamoto

Abstract

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.

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  • Rihito Sakurai & Haruto Takahashi & Koichi Miyamoto, 2024. "Learning parameter dependence for Fourier-based option pricing with tensor trains," Papers 2405.00701, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2405.00701
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    References listed on IDEAS

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    1. Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
    2. Michael Kastoryano & Nicola Pancotti, 2022. "A highly efficient tensor network algorithm for multi-asset Fourier options pricing," Papers 2203.02804, arXiv.org.
    3. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
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