This paper presents a differential machine learning (DML) approach for pricing zero-days-to-expiry (0DTE) options under the Bates stochastic-volatility jump-diffusion model. The key innovation is a neural network architecture that predicts a maturity-gated variance correction within a Black–Scholes formula, ensuring the correct short-maturity limit and reducing the approximation burden in the near-singular region. The model is trained jointly on option prices and Greeks (delta, gamma, vega) obtained via automatic differentiation, combined with a PIDE-residual penalty and no-arbitrage constraints. To address the identifiability issue of the jump term in residual-based training, the authors introduce a three-stage procedure: first training the price network, then training a separate jump-operator network against a numerical proxy, and finally jointly fine-tuning both networks with a self-consistency penalty.

Numerical experiments demonstrate that the three-stage model achieves superior accuracy in delta and vega compared to price-only or one-stage DML baselines, while maintaining comparable pricing errors. The jump-term approximation is significantly improved, with the three-stage model reducing jump-term RMSE by nearly an order of magnitude relative to the one-stage residual-regularized model. One-day delta hedging tests show that the DML-based hedges produce P&L distributions nearly identical to those using true Greeks, even under stressed parameters with high jump intensity. The method also provides substantial computational speedups over Fourier-based benchmarks, making it suitable for real-time pricing and calibration. Overall, the paper demonstrates that combining DML with structured network design and multi-stage training can effectively handle the challenges of ultra-short-maturity options with jumps.