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| HAL: hal-00562488, version 1 |
| arXiv: 1102.0683 |
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| 3èmes Journées Identification et Modélisation Expérimentale, JIME'2011, Douai : France (2011) |
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| Volatility made observable at last |
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| Michel Fliess 1Cédric Join 2, 3 |
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| (2011-04-06) |
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| 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. |
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| 1: | Laboratoire d'informatique de l'école polytechnique (LIX) |
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CNRS : UMR7161 – Polytechnique - X |
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| 2: | Centre de recherche en automatique de Nancy (CRAN) |
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CNRS : UMR7039 – Université Henri Poincaré - Nancy I – Institut National Polytechnique de Lorraine (INPL) |
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| 3: | ALIEN (INRIA Saclay - Ile de France/Inria Lille - Nord Europe) |
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INRIA – Polytechnique - X – Ecole Centrale de Lille – CNRS : UMR8146 |
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| 4: | Lucid Capital Management |
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Lucid Capital Management |
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| Subject | : | Quantitative Finance/Computational Finance Quantitative Finance/Statistical Finance Computer Science/Computational Engineering, Finance, and Science Computer Science/Automatic Control Engineering Engineering Sciences/Signal and Image processing Mathematics/Logic Statistics/Methodology Computer Science/Signal and Image Processing Environmental Sciences/Environmental Engineering |
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| Time series – quantitative finance – trends – returns – volatility – beta coefficient – Sharpe ratio – Treynor ratio – forecasts – estimation techniques – numerical differentiation – nonstandard analysis |
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| Attached file list to this document: | ||||||||||
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| hal-00562488, version 1 | |
| http://hal-polytechnique.archives-ouvertes.fr/hal-00562488 | |
| oai:hal-polytechnique.archives-ouvertes.fr:hal-00562488 | |
| From: Michel Fliess | |
| Submitted on: Thursday, 3 February 2011 14:23:20 | |
| Updated on: Sunday, 17 April 2011 19:29:44 | |
