Approximation of skewed and leptokurtic return distributions

Matthias Scherer, Svetlozar T. Rachev, Young Shin Kim, Frank J. Fabozzi

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


There is considerable empirical evidence that financial returns exhibit leptokurtosis and nonzero skewness. As a result, alternative distributions for modelling a time series of the financial returns have been proposed. A family of distributions that has shown considerable promise for modelling financial returns is the tempered stable and tempered infinitely divisible distributions. Two representative distributions are the classical tempered stable and the Rapidly Decreasing Tempered Stable (RDTS). In this article, we explain the practical implementation of these two distributions by (1) presenting how the density functions can be computed efficiently by applying the Fast Fourier Transform (FFT) and (2) how standardization helps to drive efficiency and effectiveness of maximum likelihood inference.

Original languageEnglish
Pages (from-to)1305-1316
Number of pages12
JournalApplied Financial Economics
Issue number16
StatePublished - Aug 2012


  • classical tempered stable distribution
  • fast Fourier transform
  • rapidly decreasing tempered stable distribution
  • stable Paretian distribution
  • tempered infinitely divisible distribution
  • tempered stable distribution


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