Neural Jumps for Option Pricing

TL;DR

This paper introduces a neural jump stochastic differential equation model for option pricing that incorporates neural networks and Gumbel-Softmax to effectively model jump risk, showing improved accuracy over benchmarks.

Contribution

It presents a novel neural jump SDE model with a Gumbel-Softmax approach for gradient learning in jump processes, enhancing option pricing accuracy.

Findings

Neural jump model outperforms benchmark models in pricing accuracy.

Gumbel-Softmax enables gradient learning with jump processes.

Model validated on simulated data and S&P 500 options.

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.