Numerical Methods for Stable Modeling in Financial Risk Management

The seminal work of Mandelbrot and Fama, carried out in the sixties, suggested the class of alpha-stable laws as a probabilistic model of financial assets returns. Stable distributions possess several properties which make plausible their application in the field of finance - heavy tails, excess kurtosis, domains of attraction. Unfortunately working with stable laws is very much obstructed by the lack of closed-form expressions for probability density functions and cumulative distribution functions. In the current paper we review statistical and numerical techniques which make feasible the application of stable laws in practice