Mean Reversion Level Extensions of Time-Homogeneous Affine Term Structure Models

It is well-known that time-homogeneous affine term structure models are not compatible with initial forward rate curves in general. For the Vasic̆ek (1977) and Cox, Ingersoll and Ross (1985) models, time-inhomogeneous extensions compatible with any given initial forward rate curve were introduced in Hull and White (1990), and similar extensions, for short rate models in general, were introduced in Björk and Hyll (2000), Brigo and Mercurio (2001), and Kwon (2004). This paper introduces mean-reversion level extensions of timehomogeneous affine term structure models that are compatible with any given initial forward rate curve. These extensions are minimal in the sense that the system of Ricatti equations determining the bond prices remain essentially unchanged under the extension. Moreover, the extensions considered in Björk and Hyll (2000), Brigo and Mercurio (2001), and Kwon (2004), for time-homogeneous affine term structure models, are all special cases of the extensions introduced in this paper.