Yield Curve Shapes and the Asymptotic Short Rate Distribution in Affine One-Factor Models

We consider a model for interest rates, where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipovic and Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local maximum). Each case can be characterized by simple conditions on the present short rate. We give conditions under which the short rate process will converge to a limit distribution and describe the limit distribution in terms of its cumulant generating function. We apply our results to the Vasicek model, the CIR model, a CIR model with added jumps and a model of Ornstein-Uhlenbeck type

The performance of deterministic and stochastic interest rate risk measures : Another Question of Dimensions?

The efficiency of traditional and stochastic interest rate risk measures is compared under one-, two-, and three-factor no-arbitrage Gauss-Markov term structure models, and for different immunization periods. The empirical analysis, run on the German Treasury bond market from January 2000 to December 2010, suggests that: i) Stochastic interest rate risk measures provide better portfolio immunization than the Fisher-Weil duration; and ii) The superiority of the stochastic risk measures is more evident for multi-factor models and for longer investment horizons. These findings are supported by a first-order stochastic dominance analysis, and are robust against yield curve estimation errors.info:eu-repo/semantics/publishedVersio

American options and callable bonds under stochastic interest rates and endogenous bankruptcy

American options, Optimal stopping time, Convolutions, Stochastic interest rates, Callable defaultable bonds, G13,