The AI Black-Scholes: Finance-Informed Neural Network

ArXiv ID: 2412.12213 “View on arXiv”

Authors: Unknown

Abstract

In the realm of option pricing, existing models are typically classified into principle-driven methods, such as solving partial differential equations (PDEs) that pricing function satisfies, and data-driven approaches, such as machine learning (ML) techniques that parameterize the pricing function directly. While principle-driven models offer a rigorous theoretical framework, they often rely on unrealistic assumptions, such as asset processes adhering to fixed stochastic differential equations (SDEs). Moreover, they can become computationally intensive, particularly in high-dimensional settings when analytical solutions are not available and thus numerical solutions are needed. In contrast, data-driven models excel in capturing market data trends, but they often lack alignment with core financial principles, raising concerns about interpretability and predictive accuracy, especially when dealing with limited or biased datasets. This work proposes a hybrid approach to address these limitations by integrating the strengths of both principled and data-driven methodologies. Our framework combines the theoretical rigor and interpretability of PDE-based models with the adaptability of machine learning techniques, yielding a more versatile methodology for pricing a broad spectrum of options. We validate our approach across different volatility modeling approaches-both with constant volatility (Black-Scholes) and stochastic volatility (Heston), demonstrating that our proposed framework, Finance-Informed Neural Network (FINN), not only enhances predictive accuracy but also maintains adherence to core financial principles. FINN presents a promising tool for practitioners, offering robust performance across a variety of market conditions.

Keywords: option pricing, hybrid models, neural networks, stochastic volatility, Black-Scholes, Options

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper heavily employs advanced mathematical concepts including stochastic differential equations, partial differential equations, and Itô’s lemma, but provides only theoretical validation across volatility models without presenting backtests, specific datasets, or implementation details for live trading readiness.

  flowchart TD
    A["Research Goal: Hybrid Model for Option Pricing<br>Integrate Principle-Driven & Data-Driven Approaches"] --> B["Methodology: Finance-Informed Neural Network<br>FINN Architecture"]
    B --> C["Data & Inputs: Option Pricing Data<br>Black-Scholes & Heston Models"]
    C --> D["Computational Process: Train FINN with PDE Constraints<br>Simulate Market Conditions"]
    D --> E["Outcome 1: Enhanced Predictive Accuracy<br>Superior to Pure ML Models"]
    D --> F["Outcome 2: Financial Principle Adherence<br>Maintains Theoretical Rigor"]
    D --> G["Outcome 3: Robust Performance<br>Effective across Market Conditions"]