Application of Heston model and its solution to German DAX data

We compare two well-known examples of stochastic volatility models, the Heston model and the Hull–White model. We derive the stationary probability density distribution of the variance. In addition, we apply this stationary solution to the probability density distribution of the logarithmic returns by using the conditional probability density distribution. Furthermore, we compare the received solutions of the logarithmic returns with empirical high-frequency data of DAX and its stocks.