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

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  • Takayuki Sakuma

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.

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  • Takayuki Sakuma, 2026. "Differential Machine Learning for 0DTE Options with Stochastic Volatility and Jumps," Papers 2603.07600, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2603.07600
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