A Leptokurtic‐Form Birnbaum‐Saunders Distribution With Applications to Finance

ABSTRACT We propose here a new multivariate Birnbaum‐Saunders (BS‐type) distribution characterized by its leptokurtic property, making it particularly useful in the field of finance. Unlike the approach of Romeiro et al., our proposal is also based on scale mixtures of normal distributions (SMN), but with the mixing variable following a BS distribution, resulting in an asymmetric distribution. This new distribution captures leptokurtic character in the distribution, which implies heavier tails and a more pronounced peak compared to BS or StBS distributions (BS based on the Student‐t distribution), enabling more realistic modeling of financial data. The resulting multivariate BS‐type distribution is an absolutely continuous distribution whose marginal and conditional distributions have leptokurtic properties as compared to the usual univariate BS distribution. These results are a potentially necessary supplement to the recent work of Romeiro et al. This new distribution has not been discussed yet in the literature, and it enriches the family of multivariate BS distributions as it adds new features that take advantage of the presence of observations quite concentrated around the mode. By using the nice hierarchical representation, we have developed a fast and accurate EM (Expectation‐Maximization) algorithm for computing the maximum likelihood estimates, and simulation studies show its good performance, and the corresponding asymptotic properties of the estimates. Finally, we illustrate the results with a real dataset, showcasing the effectiveness and practical utility of the proposed distribution.