Yield curve shapes and the asymptotic short rate distribution in affine one-factor models
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
We consider a model for interest rates where the short rate is given under the risk-neutral measure by a time-homogeneous one-dimensional affine process in the sense of Duffie, Filipović, 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 r t . We give conditions under which the short rate process converges to a limit distribution and describe the risk-neutral limit distribution in terms of its cumulant generating function. We apply our results to the Vasiček model, the CIR model, a CIR model with added jumps, and a model of Ornstein-Uhlenbeck type.
Details
Original language | English |
---|---|
Pages (from-to) | 149-172 |
Number of pages | 24 |
Journal | Finance and stochastics |
Volume | 12 |
Issue number | 2 |
Publication status | Published - Apr 2008 |
Peer-reviewed | Yes |
Externally published | Yes |
External IDs
ORCID | /0000-0003-0913-3363/work/167706913 |
---|
Keywords
ASJC Scopus subject areas
Keywords
- Affine process, Ornstein-Uhlenbeck process, Term structure of interest rates, Yield curve