Scaling transformation and probability distributions for financial time series
The price of financial assets are, since Bachelier, considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has been reported in several works. In this letter we investigate the question of scaling transformation of price processes by establishing a new connexion between non-linear group theoretical methods and multifractal methods developed in mathematical physics. Using two sets of financial chronological time series, we show that the scaling transformation is a non-linear group action on the moments of the price increments. Its linear part has a spectral decomposition that puts in evidence a multifractal behavior of the price increments.
|Date of creation:||25 Jan 1999|
|Note:||Type of Document - PostScript; prepared on TeX; to print on PostScript-color; pages: 12; figures: included-EPS|
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- Benoit Mandelbrot, 2015.
"The Variation of Certain Speculative Prices,"
World Scientific Book Chapters,
in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78
World Scientific Publishing Co. Pte. Ltd..
- Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation for Research in Economics, Yale University.
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