Abstract:
Finite dimensional Markovian HJM term structure models provide ideal settings for the study of term
structure dynamics and interest rate derivatives where the flexibility of the HJM framework and the tractability
of Markovian models coexist Consequently, these models became the focus of a series of papers including
Carverhill (1994), Ritcbken and Sankarasubramanian (1995), Bhar and Chiarella (1997), Inui and Kijima (1998),
de long and Santa-Clara (1999), Bjork and Svensson (2001) and Chiarella and Kwon (200la). However, these
models usually required the introduction of a large number of state variables which, at first sight, did not appear
to have clear links to the market observed quantities, and the explicit realisations of the forward rate curve in
terms of the state variables were unclear. In this paper, it is shown that the forward rate curves for these models
are affine functions of the state variables, and conversely that the state variables in these models can be expressed
as affine functions of a finite number of forward rates or yields. This property is useful, for example, in the
estimation of model parameters. The paper also provides explicit formulae for the bond prices in terms of the
state variables that generalise the formulae given in Inui and Kijima (1998), and applies the framework to obtain
affine representations for a number of popular interest rate models.
