Robust Deep Hedging

21 Pages Posted: 30 Jun 2021

See all articles by Eva Lütkebohmert

Eva Lütkebohmert

University of Freiburg, Institute for Economic Research

Thorsten Schmidt

University of Freiburg

Julian Sester

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences; University of Freiburg

Date Written: June 18, 2021

Abstract

We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black-Scholes model as well as the constant elasticity of variance (CEV) model as special cases. Based on a general dynamic programming principle, we are able to link the associated nonlinear expectation to a variational form of the Kolmogorov equation which opens the door for fast numerical pricing in the robust framework.

The main novelty of the paper is that we propose a deep hedging approach which efficiently solves the hedging problem under parameter uncertainty. We numerically evaluate this method on simulated and real data and show that the robust deep hedging outperforms existing hedging approaches, in particular in highly volatile periods.

Keywords: affine processes, Knightian uncertainty, Kolmogorov equation, deep learning, robust hedging

JEL Classification: C02, C45, G13

Suggested Citation

Lütkebohmert, Eva and Schmidt, Thorsten and Sester, Julian, Robust Deep Hedging (June 18, 2021). Available at SSRN: https://ssrn.com/abstract=3869616 or http://dx.doi.org/10.2139/ssrn.3869616

Eva Lütkebohmert

University of Freiburg, Institute for Economic Research ( email )

Platz der Alten Synagoge 1
Freiburg, D-79098
Germany

Thorsten Schmidt (Contact Author)

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

Julian Sester

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

S3 B2-A28 Nanyang Avenue
Singapore, 639798
Singapore

University of Freiburg

Freiburg, D-79085
Germany

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