Is the Difference between Deep Hedging and Delta Hedging a Statistical Arbitrage?

15 Pages Posted: 31 Jul 2024 Last revised: 21 Oct 2024

See all articles by Pascal Francois

Pascal Francois

HEC Montreal - Department of Finance

Geneviève Gauthier

Department of decision Sciences and GERAD; affiliation not provided to SSRN

Frédéric Godin

Concordia University, Quebec - Department of Mathematics & Statistics

Carlos Octavio Pérez Mendoza

Concordia University

Date Written: July 30, 2024

Abstract

The recent work of Horikawa and Nakagawa (2024) claims that under a complete market admitting statistical arbitrage, the difference between the hedging position provided by deep hedging and that of the replicating portfolio is a statistical arbitrage. This raises concerns as it entails that deep hedging can include a speculative component aimed simply at exploiting the structure of the risk measure guiding the hedging optimisation problem. We test whether such finding remains true in a GARCH-based market model. We observe that the difference between deep hedging and delta hedging can be a statistical arbitrage if the risk measure considered does not put sufficient relative weight on adverse outcomes. Nevertheless, a suitable choice of risk measure can prevent the deep hedging agent from including a speculative overlay within its hedging strategy.

Keywords: Deep reinforcement learning, optimal hedging, arbitrage

JEL Classification: C45, C61, G32

Suggested Citation

Francois, Pascal and Gauthier, Genevieve and Godin, Frédéric and Pérez Mendoza, Carlos Octavio, Is the Difference between Deep Hedging and Delta Hedging a Statistical Arbitrage? (July 30, 2024). Available at SSRN: https://ssrn.com/abstract=4899809

Pascal Francois

HEC Montreal - Department of Finance ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada
514-340-7743 (Phone)
514-340-5632 (Fax)

Genevieve Gauthier

Department of decision Sciences and GERAD ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada

affiliation not provided to SSRN

Frédéric Godin (Contact Author)

Concordia University, Quebec - Department of Mathematics & Statistics ( email )

1455 De Maisonneuve Blvd. W.
Montreal, Quebec H3G 1M8
Canada

Carlos Octavio Pérez Mendoza

Concordia University ( email )

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