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Fitting Generalized Tempered Stable distribution: Fractional Fourier Transform (FRFT) Approach

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  • A. H. Nzokem
  • V. T. Montshiwa

Abstract

The paper investigates the rich class of Generalized Tempered Stable distribution, an alternative to Normal distribution and the $\alpha$-Stable distribution for modelling asset return and many physical and economic systems. Firstly, we explore some important properties of the Generalized Tempered Stable (GTS) distribution. The theoretical tools developed are used to perform empirical analysis. The GTS distribution is fitted using S&P 500, SPY ETF and Bitcoin BTC. The Fractional Fourier Transform (FRFT) technique evaluates the probability density function and its derivatives in the maximum likelihood procedure. Based on the results from the statistical inference and the Kolmogorov-Smirnov (K-S) goodness-of-fit, the GTS distribution fits the underlying distribution of the SPY ETF return. The right side of the Bitcoin BTC return, and the left side of the S&P 500 return underlying distributions fit the Tempered Stable distribution; while the left side of the Bitcoin BTC return and the right side of the S&P 500 return underlying distributions are modelled by the compound Poisson process

Suggested Citation

  • A. H. Nzokem & V. T. Montshiwa, 2022. "Fitting Generalized Tempered Stable distribution: Fractional Fourier Transform (FRFT) Approach," Papers 2205.00586, arXiv.org, revised Jun 2022.
    • Handle: RePEc:arx:papers:2205.00586
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    References listed on IDEAS

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    1. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4256-4293.
    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.
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    Cited by:

    1. Aubain Hilaire Nzokem, 2023. "Pricing European Options under Stochastic Volatility Models: Case of Five-Parameter Variance-Gamma Process," JRFM, MDPI, vol. 16(1), pages 1-28, January.
    2. A. H. Nzokem, 2023. "European Option Pricing Under Generalized Tempered Stable Process: Empirical Analysis," Papers 2304.06060, arXiv.org, revised Aug 2023.
    3. A. H. Nzokem, 2023. "Bitcoin versus S&P 500 Index: Return and Risk Analysis," Papers 2310.02436, arXiv.org.

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