["Journal of Futures Markets, EarlyView. ", "\nABSTRACT\nMotivated by the importance of jump risk in option pricing, we propose a neural jump stochastic differential equation model that integrates neural networks as parameter estimators into a conventional jump‐diffusion model. To address the incompatibility between the backpropagation algorithm and the jump process, we use the Gumbel‐Softmax method to obtain differentiable gradients for jump parameters. We evaluate the model on both simulated data and S&P 500 index options. The results show that incorporating neural jump components substantially improves pricing accuracy relative to existing benchmark models.\n"]