Interest Rate Modeling - The Potential Approach and Multi-Curve Potential Models

This thesis is concerned with interest rate modeling by means of potential approach. The contribution of this work is twofold. First, by making use of potential approach and theory of affine Markov processes, we develop a general class of rational to term structure of interest rates which we refer to as the affine rational potential model. These feature positive interest rates and analytical pricing formulae for zero-coupon bonds, caps, swaptions, and European currency options. We present some concrete to illustrate scope of affine rational potential model and calibrate a model specification to real-world market data. Second, we develop a general family of multi-curve potential models for post-crisis interest rates. Our feature positive stochastic basis spreads, positive term structures, and analytic pricing formulae for interest rate derivatives. This modeling framework is also flexible enough to accommodate negative interest rates and positive basis spreads.