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Approximation of skewed and leptokurtic return distributions

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Author Info

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

Abstract

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.

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File URL: http://hdl.handle.net/10.1080/09603107.2012.659342
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Financial Economics.

Volume (Year): 22 (2012)
Issue (Month): 16 (August)
Pages: 1305-1316

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Handle: RePEc:taf:apfiec:v:22:y:2012:i:16:p:1305-1316

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Cited by:
  1. Michele Leonardo Bianchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2013. "Tempered stable Ornstein-Uhlenbeck processes: a practical view," Temi di discussione (Economic working papers) 912, Bank of Italy, Economic Research and International Relations Area.
  2. Michele Leonardo Bianchi & Frank J. Fabozzi & Svetlozar T. Rachev, 2014. "Calibrating the Italian smile with time-varying volatility and heavy-tailed models," Temi di discussione (Economic working papers) 944, Bank of Italy, Economic Research and International Relations Area.

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