Deep learning and American options via free boundary framework

Nwankwo, Chinonso, Umeorah, Nneka ORCID: https://orcid.org/0000-0002-0307-5011, Ware, Tony and Dai, Weizhong 2024. Deep learning and American options via free boundary framework. Computational Economics 64 , pp. 979-1022. 10.1007/s10614-023-10459-3

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Abstract

We propose a deep learning method for solving the American options model with a free boundary feature. To extract the free boundary known as the early exercise boundary from our proposed method, we introduce the Landau transformation. For efficient implementation of our proposed method, we further construct an implicit dual solution framework consisting of a novel auxiliary function and free boundary equations. The auxiliary function is formulated to include the feed-forward deep neural network (DNN) output and further mimic the far boundary behaviour, smooth pasting condition, and remaining boundary conditions due to the second-order space derivative and first-order time derivative. Because the early exercise boundary and its derivative are not a priori known, the boundary values mimicked by the auxiliary function are in approximate form. Concurrently, we then establish equations that approximate the early exercise boundary and its derivative directly from the DNN output based on some linear relationships at the left boundary. Furthermore, the option Greeks are obtained from the derivatives of this auxiliary function. We test our implementation with several examples and compare them with the existing numerical methods. All indicators show that our proposed deep learning method presents an efficient and alternative way of pricing options with early exercise features.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer
ISSN:	0927-7099
Date of First Compliant Deposit:	10 October 2023
Date of Acceptance:	11 August 2023
Last Modified:	07 Nov 2024 23:15
URI:	https://orca.cardiff.ac.uk/id/eprint/162690

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