The theory of geometric stable distributions and its use in modeling financial data

It is commonly accepted that stable distributions do provide useful models for asset returns. To accommodate the possibility of market crashes, we preserve the stability of stock price changes up to a random time T, geometrically distributed. T is viewed as a moment of extreme change of the fundamentals of a financial asset. This leads to the class of geometric stable laws, partially studied by Mittnik and Rachev. Using the Yen exchange rates data, we empirically compare several distributions and find that the geometric stable distributions dominate all other models considered, including stable laws.