An unsupervised deep learning approach in solving partial integro-differential equations

TL;DR

This paper presents an unsupervised deep learning method for solving partial integro-differential equations, enabling fast and accurate option pricing and Greeks calculation without pre-labeled data.

Contribution

It introduces an unsupervised neural network approach that directly solves PIDEs related to option pricing under Levy processes, bypassing the need for labeled training data.

Findings

Neural networks can accurately solve PIDEs for option pricing.

The method provides fast computation of option values and Greeks.

Unsupervised learning reduces reliance on pre-calculated labels.

Abstract

We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning in this paper. To price options, assuming underlying processes follow Levy processes, we require to solve PIDEs. In supervised deep learning, pre-calculated labels are used to train neural networks to fit the solution of the PIDE. In an unsupervised deep learning, neural networks are employed as the solution, and the derivatives and the integrals in the PIDE are calculated based on the neural network. By matching the PIDE and its boundary conditions, the neural network gives an accurate solution of the PIDE. Once trained, it would be fast for calculating options values as well as option Greeks.