Delta Hedging in Financial Engineering: Towards a Model-Free Approach

Michel Fliess 1, 2 Cédric Join 1, 3
1 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
Abstract : Delta hedging, which plays a crucial rôle in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009. Online: http://hal.inria.fr/inria-00352834/en/) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered with the now classic Black-Scholes-Merton framework. Several convincing computer simulations are presented. Some of them are dealing with abrupt changes, i.e., jumps.
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Michel Fliess, Cédric Join. Delta Hedging in Financial Engineering: Towards a Model-Free Approach. 18th Mediterranean Conference on Control and Automation, MED'10, Jun 2010, Marrakech, Morocco. IEEE, pp.CDROM, 2010. 〈inria-00479824〉

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