Application of the Heston and Hull-White models to German Dax Data

We focus on the stochastic description of stock price dynamics and concentrate on the Heston and Hull-White models. We derive the stationary probability density distribution of the variance of both models in the case of the zero correlation coefficient. These distributions are used to calculate solutions for the logarithmic returns of the stock price for short time lags. Furthermore, we compare the received results with numerical simulations. In addition, we apply the solutions of both models to tick-by-tick German Dax data. The data are from May 1996 to December 2001. We use the probability density distributions of the logarithmic returns calculated from the data and fit them to the theoretical distributions.