A multiple curve Lévy forward rate model in a two price economy Zusammenfassung: In this thesis we combine and merge the multiple curve approach and the two price theory based on acceptability indices in a Lévy interest rate model. A multiple curve Heath Jarrow Morton (HJM) forward rate model driven by time inhomogeneous Lévy processes (a multiple curve Lévy term structure model) is presented. We find deterministic conditions which ensure the monotonicity of the curves. Explicit valuation formulas for some interest rate derivatives are established namely forward rate agreements swaps caps floors and digital options. These formulas can numerically be evaluated very fast by using the Fourier based valuation method. Furthermore we apply the two price theory to this multiple curve setting. Ask and bid model prices of caplets floorlets and digital options are derived. A general procedure how to calibrate this two price multiple curve interest rate model to market data is described. As a practical application the model is calibrated to market prices of caps for dates before and after the global financial crisis