Asymptotically-Informed Neural Networks for Black-Scholes Implied Volatility Computation

Battle Count: 94

Implied volatility computation is fundamental to options trading, hedging, and model calibration. The proposed method provides orders-of-magnitude accuracy improvements in asymptotic regimes critical for risk management and calibration. Directly applicable to production pricing pipelines, though primarily a computational tool rather than a trading strategy.

Requires careful numerically stable implementation of Black-Scholes (Mills ratio-based), multiple gating function families with specific parametrisations, Householder refinement scheme with regime-dependent objective functions. However, the architecture is well-documented, code is provided, and evaluation reduces to matrix multiplications and pointwise non-linearities once trained.

Full code and numerical results publicly available on GitHub. Detailed architectural descriptions, 40 independent training runs reported, explicit hyperparameters provided (Nf=5, Ng=64, N=128, Adam optimizer with adaptive learning rate, 150 epochs). Numerically stable Black-Scholes implementation and Householder scheme fully derived in appendices.