Pricing High-Dimensional Bermudan Options with Hierarchical Tensor Formats

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. Complexity estimates are provided as well as a description of the optimization procedures in the tensor train format. Numerical experiments illustrate the favorable accuracy of the proposed methods. The dynamical programming method yields results comparable to recent neural network based methods.