In term structure models such as the Vasicek and CIR models, the starting point is the dynamics of the short-term interest rate. The drift and volatility are specified such that the short-term interest rate is Markovian. In the HJM framework the forward rate volatility and initial forward rate curve are used to characterise the term structure. Such a specification may give rise to non-Markovian short-term interest rate dynamics. In fact many HJM-based models cannot occur in a framework of Markovian short-term interest rates. The Markovian property of the short-term interest rate is desirable since it allows for simpler numerical valuation procedures of the term structure and interest rate contingent claims since:

The term structure at time t is a function of t, maturity T and the time t short-term interest rate.

The evolution of the short-term interest rate may be modelled using a recombining tree or lattice, which has significant implications for computational efficiency.

Carverhill andJeffrey characterise restrictions on the volatility structure of forward rates that lead to Markovian short-term interest rate dynamics.