A novel heavy tail distribution of logarithmic returns of cryptocurrencies

• Published in: Finance research letters Vol. 47; p. 102574
• Main Authors: Tran, Quang Van, Kukal, Jaromir
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-06-2022
• Subjects: Cryptocurrencies; Generalized gamma distribution; Logarithmic returns; Parameter estimation; Regularization; C52; Cryptocurrencies; Parameter estimation; Logarithmic returns; C58; Regularization; C51; Generalized gamma distribution
• ISSN: 1544-6123; 1544-6131
• DOI: 10.1016/j.frl.2021.102574

We propose a novel distribution derived from the generalized gamma distribution by symmetrization and regularization around the mean. Besides location and scale parameters, the distribution has three shape parameters with many sub-models as special cases. Its parameters can be estimated by non-linear regression with parameter significance verification and sub-model testing. The applicability of this family of novel distributions is verified on returns of three cryptocurrencies and its suitability is tested by χ2 goodness of fit testing. The obtained results show that this novel distribution and its sub-models can be viable candidates for modeling the returns of cryptocurrencies.
•We propose an original distribution derived from one-sided generalized gamma distribution by symmetrization and regularization around the mean.•This distribution is capable of capturing the well-known heavy tail property of financial assets returns.•The ability of this distribution and its special cases to model returns of cryptocurrencies is verified.•We believe that this distribution can be applied to model returns of other financial assets and it is applicable in other fields.