Volatility made observable at last
Computational Finance
2011-02-07 v1 Computational Engineering, Finance, and Science
Statistical Finance
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
Cite
@article{arxiv.1102.0683,
title = {Volatility made observable at last},
author = {Michel Fliess and Cédric Join and Frédéric Hatt},
journal= {arXiv preprint arXiv:1102.0683},
year = {2011}
}