A Geometry-Aware Residual Correction of Hagan's SABR Implied Volatility Formula

Battle Count: 81

Highly relevant to quantitative trading desks dealing with interest-rate derivatives. The framework provides ~10⁴× speed-up over Monte Carlo while maintaining R²≈0.9983 accuracy, preserves positivity and analytical structure, passes static-arbitrage checks, and runs in ~550µs per batched inference. Directly applicable to real-time pricing, calibration of swaption/cap/floor volatility surfaces, and risk management. The multiplicative correction ensures the learned surface remains structurally consistent with the underlying SABR model, critical for production trading systems.

Moderate complexity. The neural network itself is a simple 3-layer MLP (64-64-32) with standard training (Adam, 100 epochs, ~2 minutes on CPU). However, the geometric feature computation requires implementing CEV transformations, hyperbolic geodesic distances, and large-deviation asymptotics. The Monte Carlo training pipeline with control-variate variance reduction, multi-strike sampling, and Euler-Maruyama discretization adds engineering complexity. The multiplicative residual with tanh-clipping is straightforward. Overall, a competent quantitative developer could implement this in 2-4 weeks.

The paper provides detailed algorithm descriptions (Algorithm 1, 2), full parameter ranges (Table 7), architecture specifications (3 hidden layers: 64-64-32, batch norm, ReLU), optimizer settings (Adam, lr=4e-3, ReduceLROnPlateau), and data generation pipeline. However, code is only available 'upon reasonable request' from the authors, and no public repository is linked. The Monte Carlo pipeline and geometric feature computations are fully specified mathematically.