On the closed form solutions for non-extensive Value at Risk

Non-extensive properties, multifractality, and inefficiency degree of the Athens Stock Exchange General Index

“…Analytical solutions of Eq. (2) near the reported values of q in the literature, to be used as a direct Value at Risk technique, have been recently obtained (Stavroyiannis, Makris, & Nikolaidis, 2009) for highfrequency data for the Dow Jones Industrial Average index. We have included in the analysis all possible extreme values and pdf asymmetries, however it should be noted that extending a typical box plot to the 0.005 percentile except a few "outliers" (Johansen & Sornette, 1998) 99.99% of the data form a symmetric structure, with the most obvious example the positive extreme point (∼13.57 standard deviations) of the daily historical difference at 10-11 December 1987.…”