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

TL;DR

The paper addresses the challenge of pricing derivatives on multiple underlying assets by constructing market-consistent, arbitrage-free marginal densities from European option quotes using the exponential Normal Inverse Gaussian (NIG) model and binding them into a joint distribution with a Gaussian copula. It then replaces the computationally intensive high-dimensional integration with Quantum Accelerated Monte Carlo (QAMC) based on Quantum Amplitude Estimation, achieving a quadratic speedup over classical Monte Carlo for both marginal density estimation and multidimensional pricing. The authors provide theoretical guarantees for cosine-series density estimation and QAMC-based pricing, and validate the framework empirically on liquid names (Credit Agricole, AXA, Michelin), showing high calibration accuracy and substantial reductions in query costs (10–100×) compared with classical methods. This work demonstrates a practical end-to-end pathway to leverage market data and quantum computing for scalable, arbitrage-consistent pricing of basket, spread, and other multivariate derivatives, with clear avenues for extending to richer dependence structures and path-dependent payoffs.

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.

Figures (6)

• Figure 1: Credit Agricole, 1-year expiry (19/12/2025), data as of 24/12/2024 with closing spot price at 12.91 EUR. Calibrated parameters: $\bar{\alpha} = 4.69, \bar{\beta} = -3.06, \bar{\delta} = 0.18$ with $\lambda = 5 \times 10^{-7}$. Left: market vs calibrated implied volatilities. Right: prior log-normal density function using ATM implied volatility vs calibrated density function.
• Figure 2: AXA, 1-year expiry (19/12/2025), data as of 24/12/2024 with closing spot price at 33.8 EUR. Calibrated parameters: $\bar{\alpha} = 5.24, \bar{\beta} = -3.26, \bar{\delta} = 0.18$ with $\lambda = 5 \times 10^{-7}$. Left: market vs calibrated implied volatilities. Right: prior log-normal density function using ATM implied volatility vs calibrated density function.
• Figure 3: Michelin, 1-year expiry (19/12/2025), data as of 24/12/2024 with closing spot price at 31.76 EUR. Calibrated parameters: $\bar{\alpha} = 6.2, \bar{\beta} = -3.31, \bar{\delta} = 0.26$ with $\lambda = 5 \times 10^{-7}$. Left: market vs calibrated implied volatilities. Right: prior log-normal density function using ATM implied volatility vs calibrated density function.
• Figure 4: Convergence in accuracy estimating $a_k$ by CMC and QAMC.
• Figure 5: NIG density and distribution functions for AXA, estimated by CMC and QAMC varying $\mathcal{K}$.

Theorems & Definitions (18)

• Proposition 2.1: Independence of the NIG price on the location parameter
• proof
• Lemma 2.2: Continuity of NIG Option Prices
• proof
• Proposition 2.3: Existence of Solution to the Regularized Calibration Problem
• proof
• Remark : Non-uniqueness
• Remark : Stability and sensitivity
• Theorem 3.1: Sklar’s Theorem nelsen2006copulas
• Remark