Machine learning for option pricing: an empirical investigation of network architectures

ArXiv ID: 2307.07657 “View on arXiv”

Authors: Unknown

Abstract

We consider the supervised learning problem of learning the price of an option or the implied volatility given appropriate input data (model parameters) and corresponding output data (option prices or implied volatilities). The majority of articles in this literature considers a (plain) feed forward neural network architecture in order to connect the neurons used for learning the function mapping inputs to outputs. In this article, motivated by methods in image classification and recent advances in machine learning methods for PDEs, we investigate empirically whether and how the choice of network architecture affects the accuracy and training time of a machine learning algorithm. We find that the generalized highway network architecture achieves the best performance, when considering the mean squared error and the training time as criteria, within the considered parameter budgets for the Black-Scholes and Heston option pricing problems. Considering the transformed implied volatility problem, a simplified DGM variant achieves the lowest error among the tested architectures. We also carry out a capacity-normalised comparison for completeness, where all architectures are evaluated with an equal number of parameters. Finally, for the implied volatility problem, we additionally include experiments using real market data.

Keywords: Option pricing, Implied volatility, Generalized highway networks, Neural networks, Heston model, Derivatives

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced neural network architectures (highway, DGM) and references PDE methods, indicating high math complexity. It conducts structured experiments with real market data and performance metrics like MSE and training time, demonstrating high empirical rigor.

  flowchart TD
    A["Research Goal: <br>Investigate impact of <br>neural network architecture <br>on option pricing"] --> B["Methodology: <br>Train & compare architectures <br>under fixed parameter budget"]
    B --> C["Data: <br>Black-Scholes & Heston models <br>+ Real Market Data"]
    C --> D["Computational Process: <br>Supervised learning of <br>Price/Implied Volatility"]
    D --> E["Key Findings:"]
    E --> F["Generalized Highway <br>Network: Best for <br>Option Pricing"]
    E --> G["Simplified DGM: <br>Lowest error for <br>Implied Volatility"]
    E --> H["Standard Feed-Forward: <br>Baseline comparison"]