Neural Jumps for Option Pricing

2025-06-05

AI Summary

To address pricing biases in options arising from inadequate modeling of jump risk, this paper proposes a neural jump-diffusion model. Methodologically, it employs neural networks to dynamically estimate both jump intensity and jump size, relaxing the static jump-structure assumptions inherent in classical models. Crucially, it introduces the Gumbel-Softmax reparameterization technique—novel in jump-process modeling—to enable end-to-end differentiable optimization over otherwise non-differentiable jump parameters. The model is trained jointly via Monte Carlo simulation and empirical market data. Empirical evaluation on S&P 500 index options and synthetic datasets demonstrates substantial improvements over benchmark models including Heston and Merton: average pricing error is reduced by 32%. This advancement enhances both accuracy and adaptability in option pricing under jump risk.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Natural Language Processing: Learning & Optimization for NLP
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: User model development and evaluation
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions

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.

Problem

• Modeling jump risk in option pricing accurately
• Making jump parameters learnable via Gumbel-Softmax
• Improving pricing accuracy with neural jump components

Innovation

• Neural jump SDE model for pricing
• Gumbel-Softmax enables jump gradient learning
• Neural components enhance pricing accuracy