Learning Parameter Dependence for Fourier-Based Option Pricing with Tensor Trains

Rihito Sakurai (), Haruto Takahashi and Koichi Miyamoto
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Rihito Sakurai: Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
Haruto Takahashi: Department of Physics, Saitama University, Saitama 338-8570, Japan
Koichi Miyamoto: Center for Quantum Information and Quantum Biology, The University of Osaka, Osaka 560-0043, Japan

Mathematics, 2025, vol. 13, issue 11, 1-16

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. In this study, we focus on another usage of the tensor train, which 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 or 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.

Keywords: tensor train; tensor train learning algorithm; Fourier-based option pricing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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