Robust deep hedging. Issue 8 (3rd August 2022)

• Record Type: Journal Article
• Authors: Lütkebohmert, Eva; Schmidt, Thorsten; Sester, Julian
• Is Part Of: Quantitative finance. Volume 22:Issue 8(2022)
• Page Start: 1465
• Page End: 1480
• Publication Date: 2022-08-03
• Subjects: Affine processes -- Knightian uncertainty -- Kolmogorov equation -- Deep learning -- Robust hedging; C02 -- C45 -- G13; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2022.2056073
• Languages: English
• ISSNs: 1469-7688

Abstract

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 highly volatile periods.