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

2026/03/08 by Takayuki Sakuma · 1 voice
Economics, Econometrics and Finance · #q-fin.CP

paper · pdf

arxiv published 2026/03/08 · arxiv updated 2026/07/13

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 and incorporating jump-intensity price sensitivity into the learning process further improves the overall model fit. We also consider a jump rough Heston model.

Citations

• Ultra-short-term volatility surfaces
• Applying Deep Learning to Calibrate Stochastic Volatility Models
• Parametric Differential Machine Learning for Pricing and Calibration
• Hedging under rough volatility
• Differential Machine Learning
• Deep Smoothing of the Implied Volatility Surface
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Multi-factor approximation of rough volatility models
• Turbocharging Monte Carlo pricing for the rough Bergomi model
• Perfect hedging in rough Heston models
• The Pricing of Options and Corporate Liabilities

Discussions

• Takayuki Sakuma: Differential Machine Learning for 0DTE Options with Stochastic Volatility and Jumps https://arxiv.org/abs/2603.07600 https://arxiv.org/pdf/2603.07600 https://arxiv.org/html/2603.07600 [bsky, 0 points, 0 comments]

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