In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the classical as well as the Lévy Libor market model, it allows in a natural way for negative interest rates and has superb calibration properties even in the presence of extremely low rates. Moreover, the measure changes along the tenor structure are simplified significantly. These properties make it an excellent base for a post-crisis multiple curve setup. Two variants for multiple curve constructions are discussed. Timeinhomogeneous Lévy processes are used as driving processes. An explicit formula for the valuation of caps is derived using Fourier transform techniques. Based on the valuation formula, we calibrate the two model variants to market data.

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Abstract. 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 nd 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, oors 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, oorlets 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 nancial crisis. CONTENTS

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