Yield curve shapes and the asymptotic short rate distribution in affine one-factor models

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

  • Martin Keller-Ressel - , Technische Universitat Wien (Autor:in)
  • Thomas Steiner - , Technische Universitat Wien (Autor:in)

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

OriginalspracheEnglisch
Seiten (von - bis)149-172
Seitenumfang24
FachzeitschriftFinance and stochastics
Jahrgang12
Ausgabenummer2
PublikationsstatusVeröffentlicht - Apr. 2008
Peer-Review-StatusJa
Extern publiziertJa

Externe IDs

ORCID /0000-0003-0913-3363/work/167706913

Schlagworte

Schlagwörter

  • Affine process, Ornstein-Uhlenbeck process, Term structure of interest rates, Yield curve