Time series generation for option pricing on quantum computers using tensor network

TL;DR

This work tackles the state-preparation bottleneck in quantum Monte Carlo pricing by introducing a Matrix Product State (MPS) based generative model for asset-price time series under the Heston model. The MPS is trained to reproduce joint distributions of price paths, enabling generation of path samples for pricing path-dependent options via classical Monte Carlo, with results converging toward the ground-truth Heston model as discretization and bond dimensions increase. The study demonstrates accurate pricing for European, Asian, and lookback options, and shows that barrier options remain more challenging, highlighting areas for further refinement. Overall, the approach provides a practical, tensor-network–driven pathway toward quantum-ready state preparation for time-series-based option pricing and sets the stage for extensions to other stochastic models and end-to-end quantum pricing workflows.

Abstract

Finance, especially option pricing, is a promising industrial field that might benefit from quantum computing. While quantum algorithms for option pricing have been proposed, it is desired to devise more efficient implementations of costly operations in the algorithms, one of which is preparing a quantum state that encodes a probability distribution of the underlying asset price. In particular, in pricing a path-dependent option, we need to generate a state encoding a joint distribution of the underlying asset price at multiple time points, which is more demanding. To address these issues, we propose a novel approach using Matrix Product State (MPS) as a generative model for time series generation. To validate our approach, taking the Heston model as a target, we conduct numerical experiments to generate time series in the model. Our findings demonstrate the capability of the MPS model to generate paths in the Heston model, highlighting its potential for path-dependent option pricing on quantum computers.

Figures (2)

• Figure 1: Probability distributions of the asset price at $t=t_1$ (left), $t_3$ (center), and $t_5$ (right) generated by the MPS models with $m=4$ (orange bar), 5 (green bar), and 6 (red bar), and the Heston model (blue curve). $D_{\rm mex}$ is fixed to 150. For the Heston model, the Kernel Density Method silverman2018density is used to draw continuous lines.
• Figure 2: Same as Figure \ref{['fig:distributions']} except that $D_{\rm max}$ is set to 64 (orange), 100 (green), and 150 (red), with $m$ fixed to 6.