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Preliminary remarks on option pricing and dynamic hedging

Author

Listed:
  • Michel Fliess

    (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 - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique)

Abstract

An elementary arbitrage principle and the existence of trends in financial time series, which is based on a theorem published in 1995 by P. Cartier and Y. Perrin, lead to a new understanding of option pricing and dynamic hedging. Intricate problems related to violent behaviors of the underlying, like the existence of jumps, become then quite straightforward by incorporating them into the trends. Several convincing computer experiments are reported.

Suggested Citation

  • Michel Fliess & Cédric Join, 2012. "Preliminary remarks on option pricing and dynamic hedging," Post-Print hal-00705373, HAL.
    • Handle: RePEc:hal:journl:hal-00705373
    Note: View the original document on HAL open archive server: https://polytechnique.hal.science/hal-00705373
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    References listed on IDEAS

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    1. Emmanuel Nicholas Barron & Robert Jensen, 1990. "A Stochastic Control Approach to the Pricing of Options," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 49-79, February.
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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. Michel Fliess & Cédric Join, 2013. "Systematic and multifactor risk models revisited," Post-Print hal-00920175, HAL.
    3. Michel Fliess & C'edric Join, 2013. "Systematic and multifactor risk models revisited," Papers 1312.5271, arXiv.org.
    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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