Pricing high-dimensional Bermudan options with hierarchical tensor formats

TL;DR

This paper introduces a hierarchical tensor-based compression technique to efficiently price high-dimensional Bermudan options, reducing computational complexity and enabling accurate results with tensorized polynomial expansions.

Contribution

It presents a novel tensor-based approach to mitigate the curse of dimensionality in Bermudan option pricing, compatible with Monte Carlo and dual martingale methods.

Findings

Reduces computational complexity for high-dimensional problems

Achieves accuracy comparable to neural network methods

Provides effective tensor train optimization procedures

Abstract

An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented. It is shown that the "curse of dimensionality" can be alleviated for the computation of Bermudan option prices with the Monte Carlo least-squares approach as well as the dual martingale method, both using high-dimensional tensorized polynomial expansions. This discretization allows for a simple and computationally cheap evaluation of conditional expectations. Complexity estimates are provided as well as a description of the optimization procedures in the tensor train format. Numerical experiments illustrate the favourable accuracy of the proposed methods. The dynamical programming method yields results comparable to recent Neural Network based methods.