Modeling Asset Returns with Alternative Stable Distributions

Stefan Mittnik, Svetlozar T. Rachev

Research output: Contribution to journalArticlepeer-review

179 Scopus citations

Abstract

In the 1960's Benoit Mandelbrot and Eugene Fama argued strongly in favor of the stable Paretian distribution as a model for the unconditional distribution of asset returns. Although a substantial body of subsequent empirical studies supported this position, the stable Paretian model plays a minor role in current empirical work. While in the economics and finance literature stable distributions are virtually exclusively associated with stable Paretian distributions, in this paper we adopt a more fundamental view and extend the concept of stability to a variety of probabilistic schemes. These schemes give rise to alternative stable distributions, which we compare empirically using S&P 500 stock return data. In this comparison the Weibull distribution, associated with both the nonrandom-minimum and geometric-random summation schemes dominates the other stable distributions considered—including the stable Paretian model.

Original languageEnglish
Pages (from-to)261-330
Number of pages70
JournalEconometric Reviews
Volume12
Issue number3
DOIs
StatePublished - Jan 1 1993

Keywords

  • Weibull distribution
  • financial modeling
  • geometric stable distribution
  • nonrandom stable distributions

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