The Heath-Jarrow-Morton framework (“HJM”) is a general framework to model the evolution of interest rate curve – instantaneous forward rate curve in particular (as opposed to simple forward rates)
The key to these techniques is the recognition that the drifts of the no-arbitrage evolution of certain variables can be expressed as functions of their volatilities and the correlations among themselves. In other words, no drift estimation is needed.
Models developed according to the HJM framework are different from the so called short-rate models in the sense that HJM-type models capture the full dynamics of the entire forward rate curve, while the short-rate models only capture the dynamics of a point on the curve (the short rate).
However, models developed according to the general HJM framework are often non-Markovian and can even have infinite dimensions. A number of researchers have made great contributions to tackle this problem. They show that if the volatility structure of the forward rates satisfy certain conditions, then an HJM model can be expressed entirely by a finite state Markovian system, making it computationally feasible. Examples include a one-factor, two state model (O. Cheyette, “Term Structure Dynamics and Mortgage Valuation”, Journal of Fixed Income, 1, 1992; P. Ritchken and L. Sankarasubramanian in “Volatility Structures of Forward Rates and the Dynamics of Term Structure”, Mathematical Finance, 5, No. 1, Jan 1995), and later multi-factor versions.