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 distribution among stable Paretian laws, However, with steeper peaks and heavier tails than normal distribution, asymmetric Laplace laws reflec t properties of empirical financial data sets much better than the normal m odel. Despite heavier than normal tails, they have finite moments of any or der. In addition, explicit analytical forms of their one-dimensional densit ies and convenient computational forms of their multivariate densities make estimation procedures practical and relatively easy to implement. Thus, as ymmetric Laplace laws provide an interesting, efficient, and user friendly alternative to normal and stable Paretian distributions for modeling financ ial data. We present an overview of the theory of asymmetric Laplace laws a nd their applications in modeling currency exchange rates. (C) 2001 Elsevie r Science Ltd. All rights reserved.