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. 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.

Dynamical low‐rank approximations of solutions to the Hamilton–Jacobi–Bellman equation

“…In order to derive an abstract DLR problem on the TT manifold, we use a variational Monte Carlo (VMC) approach. 50,51 In our setting it can be understood as an empirical least squares tensor regression based on random samples.…”