Different energy commodities show cointegrated price movements. Moreover, the movement of the term structure in time has evidence for cointegration. In this thesis, we model cointegration in a model which allows seasonality as well as jumps in the price process. This model will extend the class of geometric models. First, we analyze the behavior of ICE UK Natural Gas Futures as well as Brent Crude Oil Futures with different maturities and see that they are cointegrated within their term structure. After we excluded seasonal effects from the price movements, we notice that there exist two different states of historical volatility in time and model them in a Markov switching framework. Jumps happen correlated two each other within the different time series, hence we use thinned-out compound Poisson process to capture there behavior. Furthermore, we describe the calibration of cointegrated geometric models with a Kalman Filter and apply the model for risk management.     «

Different energy commodities show cointegrated price movements. Moreover, the movement of the term structure in time has evidence for cointegration. In this thesis, we model cointegration in a model which allows seasonality as well as jumps in the price process. This model will extend the class of geometric models. First, we analyze the behavior of ICE UK Natural Gas Futures as well as Brent Crude Oil Futures with different maturities and see that they are cointegrated within their term structur...     »