Time Deep Gradient Flow Method for pricing American options

TL;DR

This paper introduces the Time Deep Gradient Flow method for efficiently pricing multidimensional American options, extending neural network techniques to handle free-boundary PDEs with improved speed and accuracy.

Contribution

The paper extends the TDGF neural network approach to American options, demonstrating its effectiveness in high-dimensional settings and outperforming traditional Monte Carlo methods.

Findings

TDGF achieves high accuracy in pricing American options.

TDGF outperforms Monte Carlo methods in computational speed.

TDGF is faster during training compared to DGM.

Abstract

In this research, we explore neural network-based methods for pricing multidimensional American put options under the BlackScholes and Heston model, extending up to five dimensions. We focus on two approaches: the Time Deep Gradient Flow (TDGF) method and the Deep Galerkin Method (DGM). We extend the TDGF method to handle the free-boundary partial differential equation inherent in American options. We carefully design the sampling strategy during training to enhance performance. Both TDGF and DGM achieve high accuracy while outperforming conventional Monte Carlo methods in terms of computational speed. In particular, TDGF tends to be faster during training than DGM.