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

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  • Michel Fliess

    ()
    (INRIA Saclay - Ile de France - ALIEN - INRIA - Polytechnique - X - Ecole Centrale de Lille - CNRS : UMR8146, LIX - Laboratoire d'informatique de l'école polytechnique - CNRS : UMR7161 - Polytechnique - X)

  • Cédric Join

    (INRIA Saclay - Ile de France - ALIEN - INRIA - Polytechnique - X - Ecole Centrale de Lille - CNRS : UMR8146, CRAN - Centre de recherche en automatique de Nancy - CNRS : UMR7039 - Université Henri Poincaré - Nancy I - Institut National Polytechnique de Lorraine (INPL))

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    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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    Bibliographic Info

    Paper provided by HAL in its series Post-Print with number inria-00479824.

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    Date of creation: 23 Jun 2010
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    Publication status: Published - Presented, 18th Mediterranean Conference on Control and Automation, MED'10, 2010, Marrakech, Morocco
    Handle: RePEc:hal:journl:inria-00479824

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/inria-00479824/en/
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    Keywords: Financial engineering; delta hedging; dynamic hedging; trends; quick fluctuations; abrupt changes; jumps; tracking control; model-free control;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Michel Fliess & C\'edric Join, 2009. "A mathematical proof of the existence of trends in financial time series," Papers 0901.1945, arXiv.org.
    2. Michel Fliess & Cédric Join & Mamadou Mboup, 2010. "Algebraic change-point detection," Post-Print, HAL inria-00439226, HAL.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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