Asymmetric Laplace laws and modeling financial data

Asymmetric Laplace laws form a subclass of geometric stable distributions, the limiting laws in the random summation scheme with a geometric number of terms. Among geometric stable laws, they play a role analogous to that of normal distributions among stable Paretian laws. However, with steeper peaks and heavier tails than normal distribution, asymmetric Laplace laws reflect properties of empirical financial data sets much better than the normal model. Despite heavier than normal tails, they have finite moments of any order. In addition, explicit analytical forms of their one-dimensional densities and convenient computational forms of their multivariate densities make estimation procedures practical and relatively easy to implement. Thus, asymmetric Laplace laws provide an interesting, efficient, and user friendly alternative to normal and stable Paretian distributions for modeling financial data. We present an overview of the theory of asymmetric Laplace laws and their applications in modeling currency exchange rates.