🤖 AI Summary
This study addresses the insufficient accuracy and computational efficiency in pricing zero-day-to-expiration (0DTE) options and computing their Greeks under stochastic volatility with jumps. To overcome these limitations, the authors propose a differential machine learning approach that employs a single neural network to jointly output option prices and Greeks, integrating supervised signals from both prices and Greeks with residual regularization based on the underlying partial integro-differential equation (PIDE). The method features a novel three-stage training strategy, introduces a dedicated jump operator network to enhance identifiability of the jump component, and adopts a maturity-gated Black–Scholes parametrization for the price function. Numerical experiments under the Bates model demonstrate that the proposed framework achieves comparable pricing errors while significantly improving jump modeling fidelity and Greek accuracy, enabling stable intraday Delta hedging strategies and offering substantially faster computation than Fourier-based benchmarks.
📝 Abstract
We present a differential machine learning method for zero-days-to-expiry (0DTE) options under a stochastic-volatility jump-diffusion model that computes prices and Greeks in a single network evaluation. To handle the ultra-short-maturity regime, we represent the price in Black--Scholes form with a maturity-gated variance correction, and combine supervision on prices and Greeks with a PIDE-residual penalty. To make the jump contribution identifiable, we introduce a separate jump-operator network and train it with a three-stage procedure. In Bates-model simulations, the method improves jump-term approximation relative to one-stage baselines, keeps price errors close to one-stage alternatives while improving Greeks accuracy, produces stable one-day delta hedges, and is substantially faster than a Fourier-based pricing benchmark.