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

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  • Michel Fliess

    (ALIEN - Algebra for Digital Identification and Estimation - Inria Lille - Nord Europe - Inria - Institut National de Recherche en Informatique et en Automatique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique - Centrale Lille - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Cédric Join

    (ALIEN - Algebra for Digital Identification and Estimation - Inria Lille - Nord Europe - Inria - Institut National de Recherche en Informatique et en Automatique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique - Centrale Lille - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, CRAN - Centre de Recherche en Automatique de Nancy - UHP - Université Henri Poincaré - Nancy 1 - INPL - Institut National Polytechnique de Lorraine - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Michel Fliess & Cédric Join, 2010. "Delta Hedging in Financial Engineering: Towards a Model-Free Approach," Post-Print inria-00479824, HAL.
    • Handle: RePEc:hal:journl:inria-00479824
    Note: View the original document on HAL open archive server: https://inria.hal.science/inria-00479824
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    References listed on IDEAS

    as
    1. Michel Fliess & Cédric Join, 2009. "Systematic risk analysis: first steps towards a new definition of beta," Post-Print inria-00425077, HAL.
    2. Michel Fliess & C'edric Join, 2009. "A mathematical proof of the existence of trends in financial time series," Papers 0901.1945, arXiv.org.
    3. Michel Fliess & Cédric Join, 2009. "A mathematical proof of the existence of trends in financial time series," Post-Print inria-00352834, HAL.
    4. Michel Fliess & Cédric Join, 2009. "Towards new technical indicators for trading systems and risk management," Post-Print inria-00370168, HAL.
    5. Michel Fliess & Cédric Join & Mamadou Mboup, 2010. "Algebraic change-point detection," Post-Print inria-00439226, HAL.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Michel Fliess & Cédric Join, 2010. "A model-free approach to delta hedging," Working Papers inria-00457222, HAL.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. G. Rigatos & P. Siano, 2018. "Stabilization of Mortgage Price Dynamics Using a Boundary PDE Feedback Control Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(1), pages 37-56, March.
    2. Gerasimos G. Rigatos, 2016. "Boundary Control Of The Black–Scholes Pde For Option Dynamics Stabilization," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-29, June.

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    More about this item

    Keywords

    Financial engineering; delta hedging; dynamic hedging; trends; quick fluctuations; abrupt changes; jumps; tracking control; model-free control;
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