Computational Economics

, Volume 53, Issue 1, pp 51–83 | Cite as

Quantile-Based Inference for Tempered Stable Distributions

  • Hasan A. Fallahgoul
  • David Veredas
  • Frank J. FabozziEmail author


We introduce a simple, fast, and accurate way for the estimation of numerous distributions that belong to the class of tempered stable probability distributions. Estimation is based on the method of simulated quantiles (Dominicy and Veredas in J Econom 172:235–247, 2013). MSQ consists of matching empirical and theoretical functions of quantiles that are informative about the parameters of interest. In the Monte Carlo study we show that MSQ is significantly faster than maximum likelihood and the MSQ estimators can be nearly as precise as MLE’s. A Value at Risk study using 13 years of daily returns from 21 world-wide market indexes shows that the risk assessments of MSQ estimates are as good as MLE’s.


Heavy tailed distribution Tempered stable distribution Method of simulated quantiles 

JEL classification

C5 G12 



Hasan A. Fallahgoul gratefully acknowledges financial support from the Belgian Federal Science Policy Office (BELSPO) and the Marie Curie Actions from the European Commission and from the Swiss National Science Foundation Sinergia grant “Empirics of Financial Stablity” [154445]. We thank Davy Paindaveine, the editor, and two referees for insightful remarks.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Hasan A. Fallahgoul
    • 1
  • David Veredas
    • 2
    • 3
  • Frank J. Fabozzi
    • 4
    Email author
  1. 1.School of Mathematical SciencesMonash UniversityMelbourneAustralia
  2. 2.Vlerick Business SchoolGhentBelgium
  3. 3.University of GhentGhentBelgium
  4. 4.EDHEC Business SchoolLilleFrance

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