Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-05-12
Physics
Condensed Matter
Statistical Mechanics
10 pages, 4 figures, latex and ps files
Scientific paper
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.
Brachet Marc-Etienne
Taflin Erik
Tcheou Jean Marcel
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