Describing past and forecasting future asset prices has been attracting theattention of several generations of researchers. Rather than analyzing the asset pricesP t attimes t = 1, …, Tthemselves, one usually focusses on the corresponding log-returns defined by\({R}_{t}^{c} =\log ({P}_{t}) -\log ({P}_{t-1})\) fort = 2, …, T.Considering prices (and consequently log-returns) as realizations of randomvariables, it seems natural to identify the underlying data-generating probabilitydistribution. The search for an adequate model for the distribution of stockmarket returns dates back to the beginning of the twentieth century: FollowingCourtault et al. (2000), “The date March 29, 1900, should be considered as the birthdate of mathematical finance. On that day, a French postgraduate student, Louis Bachélier, successfully defended at the Sorbonne his thesis Théorie de la Spéculation. […] This pioneering analysis of the stock and option markets contains several ideas of enormous value in both...
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Fischer, M. (2011). Financial Return Distributions. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_251
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