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Comment on “Pricing of financial derivatives based on the Tsallis statistical theory” by Zhao, Pan, Yue and Zhang

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  • Tsallis, Constantino
  • Borges, Ernesto P.

Abstract

In their recent paper, Zhao, Pan, Yue and Zhang [Chaos, Solitons and Fractals 142, 110463 (2021)] have analyzed the distribution of daily returns of the 50ETF index and concluded that “the empirical distribution rejects to obey a Gaussian distribution or a Tsallis distribution”. We exhibit here that, whereas their statement is certainly correct in what concerns the Gaussian distribution, it is sensibly wrong in what concerns what they refer to as “Tsallis distribution”. Indeed, we show here that their ’real’ data are quite satisfactorily fitted by p(x)=Meq−βx2 with (q,β,M)=(1.487,7550,40).

Suggested Citation

  • Tsallis, Constantino & Borges, Ernesto P., 2021. "Comment on “Pricing of financial derivatives based on the Tsallis statistical theory” by Zhao, Pan, Yue and Zhang," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921003805
    DOI: 10.1016/j.chaos.2021.111026
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    References listed on IDEAS

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    1. Lisa Borland, 2002. "Option Pricing Formulas based on a non-Gaussian Stock Price Model," Papers cond-mat/0204331, arXiv.org, revised Sep 2002.
    2. Zhao, Pan & Pan, Jian & Yue, Qin & Zhang, Jinbo, 2021. "Pricing of financial derivatives based on the Tsallis statistical theory," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. G. Ruiz & A. F. de Marcos, 2018. "Evidence for criticality in financial data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(1), pages 1-5, January.
    4. Lisa Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 415-431.
    5. Lisa Borland, 2002. "A Theory of Non_Gaussian Option Pricing," Papers cond-mat/0205078, arXiv.org, revised Dec 2002.
    6. de Souza, AndréM.C. & Tsallis, Constantino, 1997. "Student's t- and r-distributions: Unified derivation from an entropic variational principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 236(1), pages 52-57.
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