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

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  • Christian Walter

    (LAP - Laboratoire d’anthropologie politique – Approches interdisciplinaires et critiques des mondes contemporains, UMR 8177 - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

This chapter gives an overview of the financial modeling of extreme values by using discontinuous stochastic Lévy processes. At least two distinct programs using these processes are currently established in financial modeling: the first Mandelbrot program based on stable Lévy processes and the alternative nonstable Lévy processes-based approach. I term these two programs the radical program (RP) and the pragmatic program (PP). At first, I use Sato's classification to contrast the two programs. Next I adopt a historical perspective to present to the two programs since 1960. The RP initiated huge controversies in the academic field because of the stable hypothesis. The PP began in the 1970s with explicitly renouncing the stable hypothesis. In the 1990s a new competitor appeared, called econophysics program (EP). I show that, although the PP and the EP can be traced through separate lines in the academic fields, they share the use of tempered stable processes and derive from their reliance on Mandelbrot's view. At the end, I suggest that Mandelbrot introduce the "discontinuous turn" in financial modeling of extreme values.

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  • Christian Walter, 2016. "The Extreme Value Problem in Finance: Comparing the Pragmatic Program with the Mandelbrot Program," Post-Print hal-04561141, HAL.
    • Handle: RePEc:hal:journl:hal-04561141
    DOI: 10.1002/9781118650318.ch3
    Note: View the original document on HAL open archive server: https://hal.science/hal-04561141
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    References listed on IDEAS

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