Differential Machine Learning for 0DTE Options with Stochastic Volatility and Jumps

TL;DR

This paper introduces a differential machine learning approach for pricing 0DTE options with stochastic volatility and jumps, enhancing jump-term estimation, Greeks accuracy, and computational speed.

Contribution

It develops a unified neural network framework that models option prices and Greeks, incorporating jump dynamics and maturity effects for ultra-short options.

Findings

Improves jump-term approximation over baseline methods.

Reduces errors in Greeks and stabilizes delta hedges.

Achieves significant speedups compared to Fourier benchmarks.

Abstract

We present a differential machine learning method for zero-days-to-expiry (0DTE) options under a stochastic-volatility jump-diffusion model. To handle the ultra-short-maturity regime, we express the option price in Black-Scholes form with a maturity-gated variance correction, combining supervision on prices and Greeks with a PIDE-residual penalty. Prices and Greeks are derived from a single trained pricing network, while jump-term identifiability is ensured by a jump-operator network fitted jointly in a three-stage procedure. The method improves jump-term approximation relative to one-stage baselines while maintaining comparable pricing errors. Furthermore, it reduces errors in Greeks, produces stable one-day delta hedges, and offers significant speedups over Fourier-based benchmarks. Calibration experiments demonstrate the network's efficiency as a pricer; notably, incorporating jump-intensity price sensitivity into the learning process further improves the overall model fit.