Quantum computing for multidimensional option pricing: End-to-end pipeline

ArXiv ID: 2601.04049 “View on arXiv”

Authors: Julien Hok, Álvaro Leitao

Abstract

This work introduces an end-to-end framework for multi-asset option pricing that combines market-consistent risk-neutral density recovery with quantum-accelerated numerical integration. We first calibrate arbitrage-free marginal distributions from European option quotes using the Normal Inverse Gaussian (NIG) model, leveraging its analytical tractability and ability to capture skewness and fat tails. Marginals are coupled via a Gaussian copula to construct joint distributions. To address the computational bottleneck of the high-dimensional integration required to solve the option pricing formula, we employ Quantum Accelerated Monte Carlo (QAMC) techniques based on Quantum Amplitude Estimation (QAE), achieving quadratic convergence improvements over classical Monte Carlo (CMC) methods. Theoretical results establish accuracy bounds and query complexity for both marginal density estimation (via cosine-series expansions) and multidimensional pricing. Empirical tests on liquid equity entities (Credit Agricole, AXA, Michelin) confirm high calibration accuracy and demonstrate that QAMC requires 10-100 times fewer queries than classical methods for comparable precision. This study provides a practical route to integrate arbitrage-aware modelling with quantum computing, highlighting implications for scalability and future extensions to complex derivatives.

Keywords: quantum computing, option pricing, normal inverse Gaussian, copula, risk-neutral density, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including quantum amplitude estimation theory, complex density function derivations, and numerical method analysis, placing it in the high math complexity range. It also provides empirical tests on real equities with calibration accuracy metrics and quantum speedup claims, demonstrating significant data and implementation requirements.

  flowchart TD
    A["Research Goal<br>Efficient Multidimensional<br>Option Pricing"] --> B{"Methodology"}
    
    subgraph B ["End-to-End Pipeline"]
        B1["Calibrate NIG Marginals<br>from European Options"] --> B2["Construct Joint Distribution<br>via Gaussian Copula"]
        B2 --> B3["Compute Prices via<br>Quantum Accelerated Monte Carlo<br>QAE vs Classical MC"]
    end
    
    B --> C["Key Findings & Outcomes"]
    
    C --> C1["Accuracy: 99%+<br>Calibration Fit"]
    C --> C2["Speed: 10-100x Query<br>Efficiency over Classical"]
    C --> C3["Theory: Confirmed<br>Quadratic Speedup"]