Generalized Extreme Value distribution for fitting opening/closing asset prices and returns in stock-exchange

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 another 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).