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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, LIX)

  • C'edric Join

    (INRIA Saclay - Ile de France, CRAN)

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.

Suggested Citation

  • Michel Fliess & C'edric Join, 2010. "Delta Hedging in Financial Engineering: Towards a Model-Free Approach," Papers 1005.0194, arXiv.org.
    • Handle: RePEc:arx:papers:1005.0194
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    References listed on IDEAS

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    1. Michel Fliess & Cédric Join & Mamadou Mboup, 2010. "Algebraic change-point detection," Post-Print inria-00439226, HAL.
    2. Nicole El Karoui & Monique Jeanblanc‐Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126, April.
    3. 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.
    4. Michel Fliess & Cédric Join, 2009. "Systematic risk analysis: first steps towards a new definition of beta," Post-Print inria-00425077, HAL.
    5. Michel Fliess & C'edric Join, 2009. "A mathematical proof of the existence of trends in financial time series," Papers 0901.1945, arXiv.org.
    6. Michel Fliess & Cédric Join, 2009. "A mathematical proof of the existence of trends in financial time series," Post-Print inria-00352834, HAL.
    7. Michel Fliess & Cédric Join, 2009. "Towards new technical indicators for trading systems and risk management," Post-Print inria-00370168, HAL.
    8. Michel Fliess & Cédric Join, 2010. "A model-free approach to delta hedging," Working Papers inria-00457222, HAL.
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    Citations

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    Cited by:

    1. Michel Fliess & Cédric Join & Frédéric Hatt, 2011. "Is a probabilistic modeling really useful in financial engineering? [A-t-on vraiment besoin d'un modèle probabiliste en ingénierie financière ?]," Post-Print hal-00585152, HAL.
    2. 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.
    3. Michel Fliess & C'edric Join & Fr'ed'eric Hatt, 2011. "Is a probabilistic modeling really useful in financial engineering? - A-t-on vraiment besoin d'un mod\`ele probabiliste en ing\'enierie financi\`ere ?," Papers 1104.2124, arXiv.org, revised May 2011.
    4. 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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