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Pricing of financial derivatives based on the Tsallis statistical theory

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  • Zhao, Pan
  • Pan, Jian
  • Yue, Qin
  • Zhang, Jinbo

Abstract

Asset return distributions usually have peaks, fat tails and skewed tails, because of the impact of extreme events outside financial markets. The Tsallis distribution has the peak and fat-tail characteristic, and the asymmetric jump process can fit the skewed tail of returns. Therefore, to accurately describe asset returns, we propose a price model by the use of the Tsallis distribution and a Poisson jump process, which can characterize the long-term memory and the skewness of asset returns. Moreover, using the stochastic differential theory and the martingale method, we obtain an explicit solution for pricing European options.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308559
    DOI: 10.1016/j.chaos.2020.110463
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    1. 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).
    2. A. Gómez-Águila & J. E. Trinidad-Segovia & M. A. Sánchez-Granero, 2022. "Improvement in Hurst exponent estimation and its application to financial markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-21, December.

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