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

Michel Fliess and C\'edric Join
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Michel Fliess: INRIA Saclay - Ile de France, LIX
C\'edric Join: INRIA Saclay - Ile de France, CRAN

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Abstract: Delta hedging, which plays a crucial r\^ole 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.

Date: 2010-05
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