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Volatility made observable at last

Author

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  • Michel Fliess

    (LIX)

  • C'edric Join

    (INRIA Saclay - Ile de France, CRAN)

  • Fr'ed'eric Hatt

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 & C'edric Join & Fr'ed'eric Hatt, 2011. "Volatility made observable at last," Papers 1102.0683, arXiv.org.
    • Handle: RePEc:arx:papers:1102.0683
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    File URL: http://arxiv.org/pdf/1102.0683
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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 & C'edric Join, 2013. "Systematic and multifactor risk models revisited," Papers 1312.5271, arXiv.org.
    3. Michel Fliess & Cédric Join, 2013. "Systematic and multifactor risk models revisited," Post-Print hal-00920175, HAL.
    4. 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.

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