Comment on "Pricing of financial derivatives based on the Tsallis statistical theory" by Zhao, Pan, Yue and Zhang. (July 2021)

• Record Type: Journal Article
• Authors: Tsallis, Constantino; Borges, Ernesto P.
• Is Part Of: Chaos, solitons and fractals. Volume 148(2021)
• Publication Date: 2021-07
• Subjects: Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111026
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Pricing of financial derivatives. q-Gaussian distribution. Nonadditive entropy. 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 ) = M e q − β x 2 with ( q, β, M ) = ( 1.487, 7550, 40 ) .