Paper: arXiv 2601.04049

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (43)

  1. Pricing with a Smile (1994)
  2. Riding on a Smile (1994)
  3. A Parsimonious Arbitrage-Free Implied Volatility Parameterization with Application to the Valuation of Volatility Derivatives (2004)
  4. Arbitrage-free SVI volatility surfaces (2014)
  5. Managing Smile Risk (2002)
  6. Volatility Interpolation (2011)
  7. Filling the Gaps (2011)
  8. Building Arbitrage-Free Implied Volatility: Sinkhorn’s Algorithm and Variants (2019)
and 35 more
  1. The Normal Inverse Gaussian Distribution and the Pricing of Derivatives (2009)
  2. Prices of State-Contingent Claims Implicit in Option Prices (1978)
  3. Implied Distribution as a Function of the Volatility Smile (2012)
  4. Option pricing under NIG distribution: The empirical analysis of Nikkei 225 option (2004)
  5. Calibration of the Local Volatility in a Generalized Black–Scholes Model Using Tikhonov Regularization (2003)
  6. Financial Modelling with Jump Processes (2004)
  7. Option Pricing Models with Jumps: Integro‐Differential Equations and Inverse Problems (2004)
  8. An Introduction to Copulas (2006)
  9. Trigonometric Series (1959)
  10. Chebyshev and Fourier Spectral Methods (2001)
  11. Spectral Methods in MATLAB (2000)
  12. A Novel Pricing Method for European Options Based on Fourier–Cosine Series Expansions (2008)
  13. Quantum speedup of Monte Carlo methods (2015)
  14. Quantum Amplitud Amplification and Estimation (2002)
  15. Monte C arlo Methods in Financial Engineering (2004)
  16. NEASQC: Financial Applications (2024) — link
  17. Real Quantum Amplitude Estimation (2023)
  18. Alternative Pipeline for Option Pricing Using Quantum Computers (2025)
  19. Modified iterative quantum amplitude estimation is asymptotically optimal (2023)
  20. A Survey on Quantum Computational Finance for Derivatives Pricing and VaR (2022)
  21. Creating superpositions that correspond to efficiently integrable probability distributions (2002) — link
  22. Option pricing using quantum computers (2020)
  23. Efficient State Preparation for Quantum Amplitude Estimation (2021) — link
  24. Linear-depth quantum circuits for loading F ourier approximations of arbitrary functions (2023) — link
  25. Quantum generative adversarial networks for learning and loading random distributions (2019)
  26. L'evy Processes in Finance: Pricing Financial Derivatives (2003)
  27. Option Valuation Using the Fast Fourier Transform (1999) — link
  28. Option pricing with L egendre polynomials (2017) — link
  29. Copula Methods in Finance (2004) — link
  30. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993) — link
  31. The CTMC–Heston model: calibration and exotic option pricing with SWIFT (2021) — link
  32. Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs (2013) — link
  33. Quantum computing for finance: overview and prospects (2019) — link
  34. Calibration of Local Volatility Model with Stochastic Interest Rates by Efficient Numerical PDE Methods (2019) — link
  35. Quantum machine learning methods for F ourier-based distribution estimation with application in option pricing (2025)

0 of 43 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.