Volatility made observable at last

Michel Fliess, Cédric Join () and Frédéric Hatt
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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 - Centre Inria de l'Université de Lille - Inria - Institut National de Recherche en Informatique et en Automatique - Centre Inria de Saclay - 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

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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.

Keywords: Time series; quantitative finance; trends; returns; volatility; beta coefficient; Sharpe ratio; Treynor ratio; forecasts; estimation techniques; numerical differentiation; nonstandard analysis (search for similar items in EconPapers)
Date: 2011-04-06
New Economics Papers: this item is included in nep-ets and nep-fmk
Note: View the original document on HAL open archive server: https://polytechnique.hal.science/hal-00562488v1
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Citations: View citations in EconPapers (4)

Published in 3èmes Journées Identification et Modélisation Expérimentale, JIME'2011, Apr 2011, Douai, France. pp.CDROM

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