The objective of this thesis is to give an overview over stock price, returns, stylized facts, indices and Kernel Density Estimator, which can be used to estimate the unknown density function f. Central questions include, what is a stock price? How is the return defined? What is the definition of the adjusted stock price and how does it affect the stock price? Are the returns normally distributed? Is the distribution of returns symmetric? According to which criteria are the companies, which are contained in the DAX, being chosen? But especially: How can the Kernel Density Estimator be constructed? Is the Kernel Density Estimator dependent on the choice of the kernel or the bandwidth? A interesting fact is that returns have periods of higher volatility and periods of lower volatility. With the regard to the selection of the bandwidth of the Kernel Density Estimator, it is important to take into account, that when the density function f gets smoother, (i.e the density function f should be m-times continuously differentiable for a integer m in N large enough), the mean integrated square error of the approximation sequence of the kernel density estimator, which is a good criterion for the bandwidth selection, approaches the order O(n-1 ). But how can we select the bandwidth? Is there a method to get a bandwidth or can it be selected by eye? Furthermore, how can it be determined whether the selected bandwidth is either good or far away from the optimal bandwidth?      «

The objective of this thesis is to give an overview over stock price, returns, stylized facts, indices and Kernel Density Estimator, which can be used to estimate the unknown density function f. Central questions include, what is a stock price? How is the return defined? What is the definition of the adjusted stock price and how does it affect the stock price? Are the returns normally distributed? Is the distribution of returns symmetric? According to which criteria are the companies, which are...     »