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

2007/04/04 by Keller-Ressel, Martin, Steiner, Thomas
#60J25 #91B28 #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR)

paper · doi:10.48550/arxiv.0704.0567

Abstract

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.

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