Stable Distributions

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Abstract

In the pages set out below we explore stable distributions. A special case is the normal distribution. Stable distributions are also called Levy stable or (if not normal) stable Paretian distributions. Stable distributions other than the normal distribution are fat-tailed and may be skewed. As with the normal distribution there are theoretical justifications for using them to model financial data, if the returns on the exposures being modelled can be expected to arise from a large number of smaller innovations with suitable characteristics.

Contents

1.       Introduction

2.       Parameterisation of stable distributions

3.       Other features

4.       The Generalised Central Limit Theorem

Nomenclature

References

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