Volatility made observable at last

Michel Fliess (1) , Cédric Join (2, 3) , Frédéric Hatt (4)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 CRAN - Centre de Recherche en Automatique de Nancy
3 ALIEN - Algebra for Digital Identification and Estimation
4 Lucid Capital Management

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

Domains: Computational Finance [q-fin.CP]; Statistical Finance [q-fin.ST]; Computational Engineering, Finance, and Science [cs.CE]; Automatic Control Engineering; Signal and Image processing; Logic [math.LO]; Methodology [stat.ME]; Signal and Image Processing; Environmental Engineering

Michel Fliess, Cédric Join, Frédéric Hatt. Volatility made observable at last. 3èmes Journées Identification et Modélisation Expérimentale, JIME'2011, Apr 2011, Douai, France. pp.CDROM. ⟨hal-00562488⟩