Asymptotically-informed neural networks for Black-Scholes implied volatility computation

RESUMO

The computation of Black-Scholes implied volatility is a fundamental task in quantitative finance, underpinning option valuation, model calibration and risk management. Although implied volatility is routinely used in practice, the inversion of the pricing formula remains a challenging numerical problem, particularly in asymptotic regimes corresponding to extreme prices, strikes or maturities, where the inverse map becomes highly sensitive to perturbations of price. In this paper, we introduce a new family of asymptotically-informed neural-network architectures for implied-volatility computation. Exploiting the distinct behaviours of the function in different volatility regimes, we propose a family that learn a trainable partition of price-log-moneyness domain through a system of gating functions and combines specialised local approximations within each region. Extensive numerical experiments demonstrate that proposed models consistently outperform standard feed-forward neural networks across a wide range of parameter domains, often by several orders of magnitude in relative accuracy while maintaining excellent generalisation properties. Furthermore, the outputs provide highly accurate initial guesses for third-order Householder scheme, allowing near machine-precision computations after only two refinement iterations.