Boosting Binomial Exotic Option Pricing with Tensor Networks

TL;DR

This paper introduces tensor network techniques, specifically Matrix Product States, to significantly improve the efficiency of pricing complex exotic options like Asian and multi-asset American basket options, reducing computational complexity.

Contribution

It combines binomial pricing with tensor networks, achieving linear scaling and enhanced efficiency for exotic option pricing, which surpasses traditional methods.

Findings

Tensor network methods scale linearly with parameters.

Significant reduction in computational complexity.

Effective handling of up to 8 correlated assets.

Abstract

Pricing of exotic financial derivatives, such as Asian and multi-asset American basket options, poses significant challenges for standard numerical methods such as binomial trees or Monte Carlo methods. While the former often scales exponentially with the parameters of interest, the latter often requires expensive simulations to obtain sufficient statistical convergence. This work combines the binomial pricing method for options with tensor network techniques, specifically Matrix Product States (MPS), to overcome these challenges. Our proposed methods scale linearly with the parameters of interest and significantly reduce the computational complexity of pricing exotics compared to conventional methods. For Asian options, we present two methods: a tensor train cross approximation-based method for pricing, and a variational pricing method using MPS, which provides a stringent lower bound on option prices. For multi-asset American basket options, we combine the decoupled trees technique with the tensor train cross approximation to efficiently handle baskets of up to $m = 8$ correlated assets. All approaches scale linearly in the number of discretization steps $N$ for Asian options, and the number of assets $m$ for multi-asset options. Our numerical experiments underscore the high potential of tensor network methods as highly efficient simulation and optimization tools for financial engineering.