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Recent studies about cryptocurrency returns show that its distribution can behighly-peaked, skewed, and heavy-tailed, with a large excess kurtosis. Toaccommodate all these peculiarities, we propose the asymmetric Laplace scalemixture (ALSM) family of distributions. Each member of the family is obtainedby dividing the scale parameter of the conditional asymmetric Laplace (AL)distribution by a convenient mixing random variable taking values on all orpart of the positive real line and whose distribution depends on a parametervector $\boldsymbol{\theta}$ providing greater flexibility to the resultingALSM. Advantageously with respect to the AL distribution, the members of ourfamily allow for a wider range of values for skewness and kurtosis. Forillustrative purposes, we consider different mixing distributions; they giverise to ALSMs having a closed-form probability density function where the ALdistribution is obtained as a special case under a convenient choice of$\boldsymbol{\theta}$. We examine some properties of our ALSMs such ashierarchical and stochastic representations and moments of practical interest.We describe an EM algorithm to obtain maximum likelihood estimates of theparameters for all the considered ALSMs. We fit these models to the returns oftwo cryptocurrencies, considering several classical distributions forcomparison. The analysis shows how our models represent a valid alternative tothe considered competitors in terms of AIC, BIC, and likelihood-ratio tests.

Asymmetric Laplace scale mixtures for the distribution of cryptocurrency returns