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Approximation of skewed and leptokurtic return distributions

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  • 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.

Suggested Citation

  • Matthias Scherer & Svetlozar T. Rachev & Young Shin Kim & Frank J. Fabozzi, 2012. "Approximation of skewed and leptokurtic return distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 22(16), pages 1305-1316, August.
    • Handle: RePEc:taf:apfiec:v:22:y:2012:i:16:p:1305-1316
    DOI: 10.1080/09603107.2012.659342
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    Citations

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    Cited by:

    1. Slim, Skander & Koubaa, Yosra & BenSaïda, Ahmed, 2017. "Value-at-Risk under Lévy GARCH models: Evidence from global stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 46(C), pages 30-53.
    2. Michele Leonardo Bianchi, 2014. "Are the log-returns of Italian open-end mutual funds normally distributed? A risk assessment perspective," Temi di discussione (Economic working papers) 957, Bank of Italy, Economic Research and International Relations Area.
    3. Hasan Fallahgoul & Gregoire Loeper, 2021. "Modelling tail risk with tempered stable distributions: an overview," Annals of Operations Research, Springer, vol. 299(1), pages 1253-1280, April.
    4. Julio Mulero & Miguel A. Sordo & Marilia C. de Souza & Alfonso Suárez‐LLorens, 2017. "Two stochastic dominance criteria based on tail comparisons," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(6), pages 575-589, November.
    5. J. Hambuckers & C. Heuchenne, 2017. "A robust statistical approach to select adequate error distributions for financial returns," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 137-161, January.
    6. 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.
    7. Michele Bianchi & Frank Fabozzi, 2014. "Discussion of ‘on simulation and properties of the stable law’ by Devroye and James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 353-357, August.
    8. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.
    9. Gong, Xiaoli & Zhuang, Xintian, 2017. "Pricing foreign equity option under stochastic volatility tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 83-93.
    10. Gong, Xiaoli & Zhuang, Xintian, 2017. "Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 148-159.
    11. Michele Leonardo Bianchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2018. "Calibrating the Italian Smile with Time-Varying Volatility and Heavy-Tailed Models," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 339-378, March.
    12. Peter Bossaerts & Shijie Huang & Nitin Yadav, 2020. "Exploiting Distributional Temporal Difference Learning to Deal with Tail Risk," Risks, MDPI, vol. 8(4), pages 1-20, October.

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