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The Volcano Distribution with an Application to Stock Market Returns

Author

Listed:
  • Naaman, Michael

    (Christensen Associates)

  • Sickles, Robin

    (Rice University)

Abstract

Power-law distributions have a wide range of applications including physics, economics, and biology. We derive a new family of densities with support on the real line which obeys a broken power law called the volcano distribution. An estimation procedure is also outlined. The volcano density is very flexible as it can be unbounded or bimodal. It allows for an infinite mean or an undefined mean. The complexity of this distribution calls for a novel semiparametric estimation approach which we apply to stock market returns data.

Suggested Citation

  • Naaman, Michael & Sickles, Robin, 2015. "The Volcano Distribution with an Application to Stock Market Returns," Working Papers 15-020, Rice University, Department of Economics.
    • Handle: RePEc:ecl:riceco:15-020
    as

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    References listed on IDEAS

    as
    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    2. Michael Grabchak & Gennady Samorodnitsky, 2010. "Do financial returns have finite or infinite variance? A paradox and an explanation," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 883-893.
    3. Qi-Man Shao & Hao Yu & Jun Yu, 2001. "Do Stock Returns Follow a Finite Variance Distribution?," Annals of Economics and Finance, Society for AEF, vol. 2(2), pages 467-486, November.
    4. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
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