Time Deep Gradient Flow Method for pricing American options
This work addresses efficient pricing of American options in finance, but it is incremental as it builds on existing neural network methods.
The researchers tackled pricing multidimensional American options by extending the Time Deep Gradient Flow method to handle free-boundary PDEs, achieving high accuracy and outperforming Monte Carlo methods in computational speed, with TDGF being faster than DGM during training.
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.