Paper: arXiv 2512.16115

Authors: Liying Zhang, Ying Gao

Abstract

The increasing need for rapid recalibration of option pricing models in dynamic markets places stringent computational demands on data generation and valuation algorithms. In this work, we propose a hybrid algorithmic framework that integrates the smooth offset algorithm (SOA) with supervised machine learning models for the fast pricing of multiple path-independent options under exponential Lévy dynamics. Building upon the SOA-generated dataset, we train neural networks, random forests, and gradient boosted decision trees to construct surrogate pricing operators. Extensive numerical experiments demonstrate that, once trained, these surrogates achieve order-of-magnitude acceleration over direct SOA evaluation. Importantly, the proposed framework overcomes key numerical limitations inherent to fast Fourier transform-based methods, including the consistency of input data and the instability in deep out-of-the-money option pricing.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced stochastic calculus and Fourier transform theory for Lévy processes, indicating high mathematical complexity. It includes extensive numerical experiments comparing ML surrogates to direct SOA evaluation, demonstrating practical acceleration and data handling, reflecting strong empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Fast & Stable Option Pricing<br>under Exponential Lévy Dynamics"] --> B["Methodology: Hybrid Framework<br>Smooth Offset Algorithm (SOA) + ML Surrogates"]
  B --> C["Data Generation:<br>SOA Dataset for<br>Multiple Path-Independent Options"]
  C --> D["Model Training:<br>Neural Networks, Random Forests,<br>Gradient Boosted Trees"]
  D --> E["Inference:<br>Surrogate Pricing Operators<br>(Post-Training)"]
  E --> F["Outcomes:<br>Order-of-Magnitude Speedup<br>Stability in Deep OTM Pricing<br>Overcoming FFT Limitations"]