Paper: arXiv 2505.09459

Authors: Robert Scriba, Yuying Li, Jingbo B Wang

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents advanced quantum algorithms involving amplitude estimation, state preparation, and higher-dimensional simulations, indicating high mathematical complexity. However, it lacks any implementation details, backtesting, or empirical data, focusing purely on theoretical algorithmic development.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Quantum Monte Carlo Pricing<br>without Oracles/Assumptions"] --> B["Methodology<br>Self-Contained Quantum Algorithm"]
  B --> C["Input<br>Exponentially Many Asset Paths"]
  C --> D["Computational Process<br>Quantum Parallel Simulation"]
  D --> E["Output<br>High-Accuracy Stock Price Distribution"]
  E --> F["Key Finding 1<br>Pricing Non-Vanilla Basket Options"]
  E --> G["Key Finding 2<br>American Options & Risk Analysis"]
  F --> H["Outcome<br>Scalable High-Dimensional<br>Computational Advantage"]
  G --> H