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Renyi entropy based design of heavy tailed distribution for return of financial assets

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  • Van Tran, Quang
  • Kukal, Jaromir

Abstract

It is well-known that returns of financial assets exhibit heavy tail property and there has been no distribution which can reliably capture this characteristic so far. To contribute to the solution of this problem, we derive a new heavy tail distribution using the maximum entropy principle for Renyi entropy under the absolute moment constraints. Our newly derived distribution with two shape parameters forms a family of distributions. They are smooth, scaleable, symmetric and may be heavy tailed if their shape parameter attains the appropriate value. As a result, parameters of this distribution can be estimated by maximum likelihood estimation technique. The ability of the derived distribution to model the heavy tail property of financial assets is verified on a range of financial instruments. The results we obtained show that it can be a better option for modeling the returns of financial assets compared to other well-known heavy tailed distributions.

Suggested Citation

  • Van Tran, Quang & Kukal, Jaromir, 2024. "Renyi entropy based design of heavy tailed distribution for return of financial assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    • Handle: RePEc:eee:phsmap:v:637:y:2024:i:c:s0378437124000396
    DOI: 10.1016/j.physa.2024.129531
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    References listed on IDEAS

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    1. Park, Sung Y. & Bera, Anil K., 2009. "Maximum entropy autoregressive conditional heteroskedasticity model," Journal of Econometrics, Elsevier, vol. 150(2), pages 219-230, June.
    2. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    3. Tata Subba Rao & Granville Tunnicliffe Wilson & Andrew Harvey & Rutger-Jan Lange, 2017. "Volatility Modeling with a Generalized t Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 175-190, March.
    4. Alex Dytso & Ronit Bustin & H. Vincent Poor & Shlomo Shamai, 2018. "Analytical properties of generalized Gaussian distributions," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-40, December.
    5. Cassio Neri & Lorenz Schneider, 2012. "Maximum entropy distributions inferred from option portfolios on an asset," Finance and Stochastics, Springer, vol. 16(2), pages 293-318, April.
    6. Tanaka, Ken’ichiro & Toda, Alexis Akira, 2013. "Discrete approximations of continuous distributions by maximum entropy," Economics Letters, Elsevier, vol. 118(3), pages 445-450.
    7. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    8. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
    9. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    10. Eryiğit, Mehmet & Çukur, Sadik & Eryiğit, Resul, 2009. "Tail distribution of index fluctuations in World markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(9), pages 1879-1886.
    11. Benoit Mandelbrot, 1962. "Paretian Distributions and Income Maximization," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 76(1), pages 57-85.
    12. Tran, Quang Van & Kukal, Jaromir, 2022. "A novel heavy tail distribution of logarithmic returns of cryptocurrencies," Finance Research Letters, Elsevier, vol. 47(PA).
    13. Federica De Domenico & Giacomo Livan & Guido Montagna & Oreste Nicrosini, 2023. "Modeling and Simulation of Financial Returns under Non-Gaussian Distributions," Papers 2302.02769, arXiv.org.
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    More about this item

    Keywords

    Renyi entropy; Maximum entropy principle; Heavy tail distribution; Returns of financial assets; MLE parameter estimation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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