Numerical Methods for Stable Modeling in Financial Risk Management

Abstract

The seminal work of Mandelbrot and Fama, carried out in the 1960s, suggested the class of α-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.