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

TL;DR

This paper introduces a tensor train learning approach to efficiently approximate parameter-dependent functions in Fourier-based multi-asset option pricing, significantly reducing computational complexity while maintaining accuracy.

Contribution

The paper presents a novel tensor train learning method to accelerate Fourier transform-based option pricing by approximating parameter dependence, outperforming Monte Carlo methods.

Findings

Outperforms Monte Carlo in speed and accuracy for up to 11 assets.

Effectively compresses high-dimensional functions in option pricing.

Reduces computational complexity in multi-asset option valuation.

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.