On the Limitations of Neural Networks for Option Pricing: Analysis of Volatility Regime Sensitivity

Recent work demonstrates neural networks' theoretical ability to approximate option pricing functions, but empirical evidence regarding robustness to market regime shifts remains limited. Motivated by practical scenarios where the classical deterministic Black-Scholes equation becomes computationally challenging in high-dimensional settings or under complex market conditions, we examine neural network performance during volatility regime transitions. Models trained on low-volatility regimes ($\sigma=0.2$) show significant errors under higher volatility ($\sigma=0.3$). We provide detailed theoretical and empirical analyses indicating that these errors reflect fundamental representational limits of current architectures rather than optimization issues.