Statistical Stability in Financial Modeling

Abstract

In this paper, a theory of different stability concepts is developed including α-stability, max- stability and pot-stability. Special cases of stable distributions are introduced with some detail. The properties of heavy-tailedness and asymmetry together with the real line support encouraged in trusting stable distributions and considering them an attractive reliable environment in financial modeling. Modeling procedures are applied on real data of size 600 from the DAX portfolio3 restricted to the financial factors such as profitability, as a ratio of the net income to total assets and net income to sales, leverage , obtained by dividing the equity to total assets, and turnover expressed as a ratio of the sales to total assets. Risk measures such as value at risk and expected shortfall are also modeled via the POT-stable distributions.