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Generalized extreme value distribution for fitting opening/closing asset prices and returns in stock-exchange
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Generalized extreme value distribution for fitting opening/closing asset prices and returns in stock-exchange
C. Combes1 and A. Dussauchoy2 
| (1) |
EURISE Laboratory, University of Jean Monnet, 23 Rue du Docteur Paul Michelon, 42023 Saint-Etienne cedex 2, France |
| (2) |
PRISMa Laboratory, Bât Nautibus, University of Claude Bernard, Lyon 1, 43 bd du 11 novembre 1918, 69622 Villeurbanne cedex, France |
Abstract Robust estimation of stock-exchange fluctuations is a challenging problem. The accuracy of statistical extrapolation is fairly
sensitive to both model and sampling error. Using the opening/closing quotation and return data (concerning stock-exchange),
this paper presents a comparative assessment using various theoretical distributions: Normal, LogNormal, Gamma, Gumbel, Weibull,
Generalized Extreme Value (GEV).
We used GEV distribution in an other context than extreme value theory (indeed dedicated to this domain). From the empirical
distribution on short periods (3, 6, 9 and 12 months), we prove that GEV distribution allows to correctly fit returns and
opening/closing quotations (without studying only the behaviour of maxima or minima in a sample, but overall of the sample)
by comparison with the other distributions. This paper focuses on the GEV distribution in the univariate case. Following a
review of the literature, univariate GEV distribution is applied to a series of daily stock-exchange of TOTAL oil company.
We illustrate this article with the opening/closing quotations minus the moving average of the five last days and the returns
of this company on short and medium terms (3, 6, 9, 12 months moving forward 1 month).
Keywords GEV Distribution - opening/closing asset prices and returns - fitting empirical data of stock-exchange to theoretical probability laws
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