## Simulation Methods

The output of any simulation of stock prices is a time series which can be used for the investigation of further financial problems (e.g., asset pricing, evaluation of trading strategies, description of price movements, forecasting and portfolio management). Several methods to simulate stock prices are described in the scientific literature. Mainly the used methods can be categorized by the type of the generated time series:

- Real historical time series (Classical Back-Testing)
- Financial model based artifical time series (Random walk models as Brownian Motion and Binomial Model)
- Hybrid time series (Resampling Methods: Bootstrap, Jack Knife)

## Simulation and Forecasting

The methods of simulation of stock prices are not able to produce point estimations of the future. They are not able to determine a certain future price *q* in the *k-*th trading period. Rather, they can be used to produce an interval estimation of the future price *q*. For example, the price of an asset in the *k*-th trading period will be between *q_min* and *q_max* with a probability of *α* percent. *α* is always lower than 1.