Learning parameter dependence for Fourier-based option pricing with tensor trains

Paper: arXiv 2405.00701

Abstract

A long-standing issue in mathematical finance is the speed-up of option pricing, especially for multi-asset options. A recent study has proposed to use tensor train learning algorithms to speed up Fourier transform (FT)-based option pricing, utilizing the ability of tensor trains to compress high-dimensional tensors. Another usage of the tensor train is to compress functions, including their parameter dependence. Here, we propose a pricing method, where, by a tensor train learning algorithm, we build tensor trains that approximate functions appearing in FT-based option pricing with their parameter dependence and efficiently calculate the option price for the varying input parameters. As a benchmark test, we run the proposed method to price a multi-asset option for the various values of volatilities and present asset prices. We show that, in the tested cases involving up to 11 assets, the proposed method outperforms Monte Carlo-based option pricing with $10^6$ paths in terms of computational complexity while keeping better accuracy.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces advanced tensor train decomposition and learning algorithms (TCI) with dense mathematical formulation, earning a high math score; it includes concrete computational benchmarks on multi-asset options with 11 assets and claims performance gains over Monte Carlo, which provides empirical rigor but lacks real-world data or code disclosure.

Research Flowchart

  flowchart TD
  A["Research Goal: Speed-up<br>Multi-asset Option Pricing"] --> B["Methodology: Tensor Train Learning<br>for Fourier-based Pricing"]
  B --> C{"Input Data: Multi-asset Option<br>Parameter Sets"}
  C --> D["Compute Tensor Train<br>Approximations"]
  D --> E["Efficiently Calculate<br>Option Prices"]
  E --> F{"Benchmarking"}
  F -->|Monte Carlo (10^6 paths)| G["Standard Method"]
  F -->|Proposed Method| H["Optimized Method"]
  G --> I["Key Findings"]
  H --> I
  I --> J["Proposed method outperforms<br>Monte Carlo in computational complexity<br>for up to 11 assets"]
  I --> K["Maintains higher accuracy<br>at lower cost"]

Cited References (56)

1. A highly efficient tensor network algorithm for multi-asset Fourier options pricing (2022) — link
2. $O(d\log N)$ -Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling (2011) — link
3. Tensor Numerical Methods in Scientific Computing (2018) — link
4. The ITensor Software Library for Tensor Network Calculations (2022) — link
5. tf-quant-finance (2023)
6. Options futures and other derivatives (2003)
7. Stochastic calculus for finance I & II (2004)
8. Quantum computing for finance (2023) — link

0 of 56 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.