Paper: arXiv 2603.07600

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a novel neural network architecture for zero-days-to-expiry (0DTE) option pricing under a stochastic volatility jump-diffusion model using Differential Machine Learning. The inclusion of a maturity-gated Black-Scholes variance correction and a decoupled jump-operator network provides an elegant solution to PINN identifiability issues. The empirical evaluation includes derivative sensitivity tests, hedging experiments, and speedup benchmarks against classical Fourier pricers.

Research Flowchart

  flowchart TD
    A["<b>Research Goal</b><br>Accurate, fast 0DTE option pricing & hedging under SVJD"] --> B["<b>Input Data</b><br>Spot, Strike, SVJD Parameters, 0DTE Regime Features"]
    
    B --> C["<b>Model Architecture</b><br>Black-Scholes form + Maturity-gated variance correction"]
    
    C --> D["<b>Three-Stage Joint Training</b><br>1. Price & Greeks Supervision<br>2. PIDE-Residual Penalty<br>3. Jump-Operator Network Fit"]
    
    D --> E["<b>Outputs & Performance</b><br>Single Pricing Network → Prices, Delta, & Vega"]
    
    E --> F["<b>Key Outcomes</b><br>• Improved jump-term identifiability<br>• Stable 1-day delta hedging<br>• Significant speedup vs. Fourier benchmark"]