# Pricing high-dimensional Bermudan options with hierarchical tensor formats

arXiv: https://arxiv.org/abs/2103.01934 · HTML: https://mlsanity.com/paper/2103.01934/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2021.

## Built on by (most cited first, 6 of 6)

- [Optimal Stopping via Randomized Neural Networks](https://mlsanity.com/paper/2104.13669/) (2021)
- [From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs](https://mlsanity.com/paper/2307.15496/) (2023)
- [A block-sparse Tensor Train Format for sample-efficient high-dimensional Polynomial Regression](https://mlsanity.com/paper/2104.14255/) (2021)
- [Functional SDE approximation inspired by a deep operator network architecture](https://mlsanity.com/paper/2402.03028/) (2024)
- [Convergence bounds for nonlinear least squares and applications to tensor recovery](https://mlsanity.com/paper/2108.05237/) (2021)
- [Convergence bounds for local least squares approximation](https://mlsanity.com/paper/2208.10954/) (2022)

## Abstract (arXiv)

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.