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

ArXiv ID: 2402.17148 “View on arXiv”

Authors: Unknown

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.

Keywords: Quantum Computing, Matrix Product State (MPS), Path-Dependent Options, Heston Model, Generative Models, Equity Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts including Matrix Product States (MPS) from tensor network theory, quantum amplitude estimation, and stochastic differential equations (Heston model), warranting a high math score. It validates the approach with numerical experiments on simulated data and classical Monte Carlo, showing empirical implementation but lacking real-market data or live backtesting, placing it in the Holy Grail quadrant.

  flowchart TD
    A["Research Goal:<br>Efficient Time Series Generation<br>for Path-Dependent Option Pricing"] --> B["Methodology:<br>Matrix Product State<br>Generative Model"]
    
    B --> C["Data & Input:<br>Heston Model<br>Parameters"]
    
    C --> D["Computational Process:<br>MPS Training & Time Series Generation"]
    
    D --> E{"Outcome"}
    E --> F1["Successful Generation<br>of Heston Paths"]
    E --> F2["Efficient State Preparation<br>for Quantum Algorithms"]
    
    F1 & F2 --> G["Key Finding:<br>Promising Path for<br>Quantum Option Pricing"]