Monte-Carlo Option Pricing in Quantum Parallel

2025-05-14

AI Summary

Classical pricing methods for high-dimensional complex financial derivatives—such as exotic basket options, American options, and portfolio risk analysis—face severe computational bottlenecks. To address this, we propose the first oracle-free, self-contained quantum Monte Carlo algorithm. Our method leverages quantum random number generation, amplitude encoding, and quantum path integral simulation to efficiently generate exponentially many asset price paths in quantum parallelism, directly reconstructing the underlying asset price distribution. Theoretically, it achieves a quadratic speedup of *O*(√*N*) and exactly recovers the Black–Scholes analytical solution. It is the first scalable quantum pricing framework demonstrated for 10-dimensional basket options and American options. Furthermore, it establishes a foundational quantum framework for portfolio risk measures—including Value-at-Risk (VaR) and Expected Shortfall (ES)—enabling exponential state-space exploration while preserving statistical fidelity.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods like Monte Carlo simulations and numerical techniques. However, as derivative complexities increase, these methods face limitations in computational power. Cases involving Non-Vanilla Basket pricing, American Options, and derivative portfolio risk analysis need extensive computations in higher-dimensional spaces, posing challenges for classical computers. Quantum computing presents a promising avenue by harnessing quantum superposition and entanglement, allowing the handling of high-dimensional spaces effectively. In this paper, we introduce a self-contained and all-encompassing quantum algorithm that operates without reliance on oracles or presumptions. More specifically, we develop an effective stochastic method for simulating exponentially many potential asset paths in quantum parallel, leading to a highly accurate final distribution of stock prices. Furthermore, we demonstrate how this algorithm can be extended to price more complex options and analyze risk within derivative portfolios.

Problem

• Pricing complex financial derivatives efficiently
• Overcoming classical computational limits in high dimensions
• Simulating quantum parallel asset paths for accuracy

Innovation

• Quantum algorithm for Monte-Carlo option pricing
• Stochastic simulation of exponential asset paths
• Extension to complex options and risk analysis