Time series generation for option pricing on quantum computers using tensor network
This work addresses the challenge of costly quantum state preparation in finance, specifically for path-dependent option pricing, but it is incremental as it builds on existing quantum algorithms with a focus on improving efficiency.
The paper tackled the problem of efficiently generating quantum states encoding probability distributions for path-dependent option pricing by proposing a Matrix Product State (MPS) as a generative model for time series, and demonstrated its capability to generate paths in the Heston model through numerical experiments.
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.