Lévy-stability-under-addition and fractal structure of markets: Implications for the investment management industry and emphasized examination of MATIF notional contract

Christian Walter ()

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Abstract: This paper presents the connection between the stable distributions and the fractal structure of markets. After having described the main concepts, we conduct an emphasized empirical examination of the Léy-stability-under-addition of the French MATIF notional contract on ten year government bonds. Following Mandelbrot's intuitions, we attempt to verify the existence of an underlying fractal structure governing the price variations, on different time intervals. The results are in the sense of Mandelbrot's intuitions: it is possible to characterize a fractal structure from one to 20 days variations (returns) of the market. This fractal structure is only perceptible using the Lévy distributions, and in this sense, the fractality of the market is associated with the Lévy stability-under-addition property. By resealing space and time, the statistical invariance of MATIF is exhibited.

Date: 1999-05
Note: View the original document on HAL open archive server: https://hal.science/hal-04578307
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Published in Mathematical and Computer Modelling, 1999, 29 (10-12), pp.37-56. ⟨10.1016/S0895-7177(99)00091-6⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04578307

DOI: 10.1016/S0895-7177(99)00091-6

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