The HJM Forward Rate Model

The forward rate models typically assume historical forward rate volatilities and an initially observed set of forward rates as model inputs the forward rate models of Heath, Jarrow, and Morton (HJM), the LIBOR market model (LMM), and the String model are preference free by construction. Since, these models exogenously specify the forward rate process, which uniquely determines the risk-neutral short rate process without requiring the specification of market prices of risks, preferences do not enter into the valuation process. It is conceptualized as double-plus HJM models, which do not impose any restrictions on the functional form of the initially observed forward rates but allow only specific functional forms for the forward rate volatility function. But such classification of existing preference-free term structure models as “HJM models” serves little purpose, especially when many of these models have been derived independently by other researchers.