Boosting Binomial Exotic Option Pricing with Tensor Networks

ArXiv ID: 2505.17033 “View on arXiv”

Authors: Maarten van Damme, Rishi Sreedhar, Martin Ganahl

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.

Keywords: tensor network methods, Matrix Product States, exotic derivatives pricing, binomial trees, multi-asset options, Derivatives

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced tensor network mathematics (Matrix Product States) and high-dimensional function approximation with bond dimensions, requiring significant theoretical expertise. However, it lacks implementation details, backtests, or statistical metrics, focusing instead on theoretical scaling and potential rather than empirical validation.

  flowchart TD
    A["Research Goal: Overcome computational<br>challenges in pricing exotic options"] --> B["Methodology: Tensor Networks<br>(Matrix Product States MPS)"]
    B --> C{"Option Type"}
    C --> D["Asian Options<br>Linear in N steps"]
    C --> E["Multi-Asset American Baskets<br>Linear in m assets"]
    D --> F["Methods: TT Cross Approx &<br>Variational MPS Pricing"]
    E --> G["Method: Decoupled Trees &<br>TT Cross Approx"]
    F & G --> H["Inputs: Market Parameters,<br>Correlation Matrices"]
    H --> I["Computational Process:<br>Linear Scaling O(N) or O(m)"]
    I --> J["Key Outcomes:<br>Efficient Pricing, Accurate Bounds,<br>Scalability up to 8 Assets"]