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

Abstract

We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning. The PIDE is employed for option pricing, when the underlying process is a Lévy process with jumps. The unsupervised deep learning approach employs a neural network as the candidate solution and trains the neural network to satisfy the PIDE. By matching the PIDE and the boundary conditions, the neural network would yield an accurate solution to the PIDE. Unlike supervised learning, this approach does not require any labels for training, where labels are typically option prices as well as Greeks. Additional singular terms are added to the neural network to satisfy the non-smooth initial conditions. Once trained, the neural network would be fast for calculating option prices as well as option Greeks.

Keywords:

• PIDE
• Lévy process
• Neural network
• Deep learning
• Option pricing

JEL Classification:

• C63

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.