Efficient option pricing with unary-based photonic computing chip and generative adversarial learning

ArXiv ID: 2308.04493 “View on arXiv”

Authors: Unknown

Abstract

In the modern financial industry system, the structure of products has become more and more complex, and the bottleneck constraint of classical computing power has already restricted the development of the financial industry. Here, we present a photonic chip that implements the unary approach to European option pricing, in combination with the quantum amplitude estimation algorithm, to achieve a quadratic speedup compared to classical Monte Carlo methods. The circuit consists of three modules: a module loading the distribution of asset prices, a module computing the expected payoff, and a module performing the quantum amplitude estimation algorithm to introduce speed-ups. In the distribution module, a generative adversarial network is embedded for efficient learning and loading of asset distributions, which precisely capture the market trends. This work is a step forward in the development of specialized photonic processors for applications in finance, with the potential to improve the efficiency and quality of financial services.

Keywords: Quantum Computing, Quantum Amplitude Estimation, Photonic Chip, Generative Adversarial Networks (GAN), Option Pricing, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is dense with advanced mathematical concepts, including quantum amplitude estimation, unary encoding, and complex linear optical circuit transformations. However, it focuses on a theoretical chip design and simulation results without presenting backtested financial data, robust statistical metrics, or code for reproducibility.

  flowchart TD
    A["Research Goal:<br>Efficient European Option Pricing"]
    B1["Input:<br>Historical Asset Data"]
    B2["Input:<br>Financial Parameters<br>S, K, T, r, σ"]
    C["Methodology:<br>Generative Adversarial Network GAN"]
    D["Computational Module:<br>Unary Photonic Quantum Chip"]
    E1["Process:<br>Distribution Loading<br>Asset Price PDF"]
    E2["Process:<br>Quantum Amplitude Estimation<br>QAE"]
    F["Key Outcomes:<br>Quadratic Speedup over Monte Carlo"]
    G["Outcome:<br>Specialized Photonic Processor<br>for Finance"]

    A --> B1
    A --> B2
    B1 --> C
    C --> E1
    B2 --> D
    E1 --> D
    D --> E2
    E2 --> F
    F --> G