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Volatility made observable at last

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

    (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, 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)

  • Frédéric Hatt

    (Lucid Capital Management - Lucid Capital Management)

Abstract

The Cartier-Perrin theorem, which was published in 1995 and is expressed in the language of nonstandard analysis, permits, for the first time perhaps, a clear-cut mathematical definition of the volatility of a financial asset. It yields as a byproduct a new understanding of the means of returns, of the beta coefficient, and of the Sharpe and Treynor ratios. New estimation techniques from automatic control and signal processing, which were already successfully applied in quantitative finance, lead to several computer experiments with some quite convincing forecasts.

Suggested Citation

  • Michel Fliess & Cédric Join & Frédéric Hatt, 2011. "Volatility made observable at last," Post-Print hal-00562488, HAL.
    • Handle: RePEc:hal:journl:hal-00562488
    Note: View the original document on HAL open archive server: https://polytechnique.hal.science/hal-00562488
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    References listed on IDEAS

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    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
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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. Michel Fliess & Cédric Join, 2013. "Systematic and multifactor risk models revisited," Post-Print hal-00920175, HAL.
    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. Michel Fliess & C'edric Join, 2013. "Systematic and multifactor risk models revisited," Papers 1312.5271, arXiv.org.

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    More about this item

    Keywords

    Time series; quantitative finance; trends; returns; volatility; beta coefficient; Sharpe ratio; Treynor ratio; forecasts; estimation techniques; numerical differentiation; nonstandard analysis;
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