Paper: arXiv 2506.05137

Authors: Duosi Zheng, Hanzhong Guo, Yanchu Liu, Wei Huang

Abstract

Recognizing the importance of jump risk in option pricing, we propose a neural jump stochastic differential equation model in this paper, which integrates neural networks as parameter estimators in the conventional jump diffusion model. To overcome the problem that the backpropagation algorithm is not compatible with the jump process, we use the Gumbel-Softmax method to make the jump parameter gradient learnable. We examine the proposed model using both simulated data and S&P 500 index options. The findings demonstrate that the incorporation of neural jump components substantially improves the accuracy of pricing compared to existing benchmark models.

Complexity vs Empirical Score

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

Why this score: The paper presents an innovative hybrid framework combining jump-diffusion SDEs with neural networks by leveraging the Gumbel-Softmax trick for backpropagation compatibility. It features both theoretical grounding and solid empirical evaluation on S&P 500 index option data.

Research Flowchart

  flowchart TD
    A[Goal: Improve Option Pricing via Neural Jump SDE] --> B[Data Inputs: Simulated Data & S&P 500 Index Options]
    B --> C[Methodology: Integrate NNs as Parameter Estimators in Jump Diffusion Model]
    C --> D[Gumbel-Softmax Trick: Enable Gradient Backpropagation for Jump Process]
    D --> E[Model Training & Calibration]
    E --> F[Findings: Neural Jump Components Substantially Improve Pricing Accuracy]

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0 of 58 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.