Stock returns and hyperbolic distributions

The four parameter family of hyperbolic distributions fits very well the daily returns of the German stocks that have been included in the DAX during the period 1974 and 1992. Estimators and confidence regions for the hyperbolic parameters are calculated from the empirical data. In particular, skewness and kurtosis can be modelled much better by hyperbolic distributions than by normal distributions. Dates of outliers are identified with economical or political events in the world. It is indicated how the hyperbolic parameters can be used to compare different stocks.