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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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    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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