Chapter 3The Extreme Value Problem in Finance: Comparing the Pragmatic Program with the Mandelbrot Program

Christian Walter

Collège détudes mondiales, Fondation Maison des sciences de l'homme, Paris, France

3.1 The Extreme Value Puzzle in Financial Modeling

The extreme value puzzle in finance has a long history (Longin, 1993; Fraga Alves and Neves, 2017). As early as in the 1950s, one noticed that the price changes presented such a phenomenon. For example, in a landmark paper published in the Journal of the Royal Statistical Society, Maurice Kendall wrote that the results from price data between 1883 and 1934 are such that “[t]he distributions are accordingly rather leptokurtic” (Kendall, 1953, 13). Seven years after, in the Food Research Institute Studies, Arnold Larson noticed that “Examination of the pattern of occurrence of all price changes in excess of three standard deviations from zero (c03-math-0001) indicated that [there is] presence in the data of an excessive number of extreme values” (Larson, 1960, 224, our italics).

The mainstream view of the extreme values of distributions considered these data as irrelevant for financial modeling. For example, Granger and Orr (1972) asserted that “[i]f the long tails of empirical distributions are of concern to the time-series analyst or econometrician, it is natural to consider reducing the importance of these tails. The most obvious approach ...

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