Learning Fourier-based parametric option pricing with tensor trains

Abstract

We address the challenge of accelerating multi-asset option pricing using tensor-train learning algorithms, a type of active machine learning.Here, we build tensor trains using a tensor train learning algorithm to approximate functions appearing in FT-based option pricing along with their parameter dependence and make a new function that takes parameters and outputs the FT-based option prices.Then, we utilize this function to 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, involving up to 11 assets.We demonstrate that our method achieves superior computational complexity and time compared to Monte Carlo methods with $10^5$ paths while maintaining comparable accuracy.