On the Inversion of the Yield Curve

This volume contains five essays on topics related to interest rate theory.The first essay, Affine Term Structures and Short-Rate Realizations of Forward Rate Models Driven by Jump-Diffusion Processes, examines the problem of determining when a given forward rate model has a short-rate realization, and when a short-rate model gives rise to an affine term structure.The second essay, On the Inversion of the Yield Curve, co-authored with Tomas Bjork, considers a general benchmark short-rate factor model of the term structure of interest rates. It is showed that the benchmark model can be extended so that the implied theoretical term structure can be fitted exactly to an arbitrary initially observed yield curve. A general formula for pricing simple contingent claims in the extended model is also provided.The third essay, An Efficient Series Expansion Approach to a Two-Factor Model of the Term Structure of Interest Rates, presents a two-factor model where both factors follow CIR-type diffusion processes. A series expansion is used to solve for discount bond prices. The model is also compared with a corresponding Gaussian model, and no substantial differences are found between the two models regarding the flexibility and shapes of the yield curves and forward rate curves they generate.The fourth essay, An Efficient Series Expansion Approach to The Balduzzi, Das, Foresi and Sundaram Model of the Term Structure of Interest Rates, revisits the model by BDFS, and apart from giving an explicit solution to discount bond prices by using a series expansion, the model is extended so that the implied theoretical term structure can be fitted exactly to an arbitrary initially observed yield curve.The fifth essay, Quasi Arbitrage-Free Discount Bond Prices in the Cox, Ingersoll and Ross Model, offers an example of a less regular solution to the term structure equation in the CIR model. This new and different solution fails to meet one of the standard regularity conditions, but only at one particular point. Under additional conditions, the solution can be interpreted as a term structure, which is referred to as a quasi arbitrage-free term structure.