IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2205.00586.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2205.00586
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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, 2024. "Fitting the seven-parameter Generalized Tempered Stable distribution to the financial data," Papers 2410.19751, arXiv.org.
    4. A. H. Nzokem, 2023. "Bitcoin versus S&P 500 Index: Return and Risk Analysis," Papers 2310.02436, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A. H. Nzokem, 2023. "European Option Pricing Under Generalized Tempered Stable Process: Empirical Analysis," Papers 2304.06060, arXiv.org, revised Aug 2023.
    2. Michael Grabchak, 2015. "Inversions of Lévy Measures and the Relation Between Long and Short Time Behavior of Lévy Processes," Journal of Theoretical Probability, Springer, vol. 28(1), pages 184-197, March.
    3. Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.
    4. Sampaio, Jhames M. & Morettin, Pedro A., 2020. "Stable Randomized Generalized Autoregressive Conditional Heteroskedastic Models," Econometrics and Statistics, Elsevier, vol. 15(C), pages 67-83.
    5. Asmerilda Hitaj & Lorenzo Mercuri & Edit Rroji, 2019. "Lévy CARMA models for shocks in mortality," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 205-227, June.
    6. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.
    7. Yunfei Xia & Michael Grabchak, 2024. "Pricing multi-asset options with tempered stable distributions," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-24, December.
    8. Walter Farkas & Ludovic Mathys & Nikola Vasiljević, 2021. "Intra‐Horizon expected shortfall and risk structure in models with jumps," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 772-823, April.
    9. A. H. Nzokem, 2023. "Bitcoin versus S&P 500 Index: Return and Risk Analysis," Papers 2310.02436, arXiv.org.
    10. Li, Hengxin & Wang, Ruodu, 2023. "PELVE: Probability Equivalent Level of VaR and ES," Journal of Econometrics, Elsevier, vol. 234(1), pages 353-370.
    11. Wied, Dominik & Dehling, Herold & van Kampen, Maarten & Vogel, Daniel, 2014. "A fluctuation test for constant Spearman’s rho with nuisance-free limit distribution," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 723-736.
    12. Tong Liu & Yanlin Shi, 2022. "Innovation of the Component GARCH Model: Simulation Evidence and Application on the Chinese Stock Market," Mathematics, MDPI, vol. 10(11), pages 1-18, June.
    13. Borak, Szymon & Misiorek, Adam & Weron, Rafał, 2010. "Models for heavy-tailed asset returns," SFB 649 Discussion Papers 2010-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. Michael Grabchak, 2021. "On the transition laws of p-tempered $$\alpha $$ α -stable OU-processes," Computational Statistics, Springer, vol. 36(2), pages 1415-1436, June.
    15. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, vol. 4(2), pages 1-28, May.
    16. Gong, Xiao-li & Zhuang, Xin-tian, 2016. "Option pricing and hedging for optimized Lévy driven stochastic volatility models," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 118-127.
    17. 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.
    18. Paolella, Marc S., 2017. "Asymmetric stable Paretian distribution testing," Econometrics and Statistics, Elsevier, vol. 1(C), pages 19-39.
    19. Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Fabozzi, Frank J., 2013. "CVaR sensitivity with respect to tail thickness," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 977-988.
    20. Roberto Baviera & Pietro Manzoni, 2024. "Fast and General Simulation of L\'evy-driven OU processes for Energy Derivatives," Papers 2401.15483, arXiv.org, revised Sep 2024.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2205.00586. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.