Abstract
This chapter considers interest rate multi-factor and whole yield curve models such as the Ho–Lee model and Heath–Jarrow–Morton family of models. A landmark development in interest-rate modeling has been the specification of the dynamics of the complete term structure. A simple approach is described in the Ho–Lee model, in which the volatility of the term structure is a parallel shift in the yield curve, the extent of which is independent of the current time and the level of current interest rates. The Ho–Lee model is not widely used, although it was the basis for the Heath–Jarrow–Morton (HJM) model. In the HJM model, the processes for the bond price and the spot rate are not independent of each other. As an arbitrage-free pricing model, it differs in crucial respects from equilibrium models. The core of the HJM model is that given a current forward rate curve and a function capturing the dynamics of the forward rate process, it models the entire term structure.
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