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Difference HJM Framework versus Short rate model Mathematically you could model this by a HJM model that is driven by three Brownian motions I do not believe that every HJM model captures the full dynamics of the entire forward curve If that were true even the poorest HJM model (namely the one you get when you start with the Ho-Lee model) could capture the full dynamics
Heath Jarrow Morton Framework - Quantitative Finance Stack Exchange HJM has its issues though: it is in general non-Markovian and infinite dimensional, making it a difficult to use in practice 'Discrete' modifications of HJM such as the Libor Market Model and Swap Market Model (SMM) address some of its practical implementation issues
3 Factor HJM model, do these factors have an economic meaning? One of the motivations for multifactor models such as Two-Factor-HW, HJM and LMM (Lobor-Market-Model) is derived from the properties of the yield curve One can run a Principal-Component-Analysis on yield-curve data in order to analyse the number of independant factors contributing to yield curve movements It has been shown that there are generally three types of movements a yield curve can
Ho-Lee short rate model under the Heath-Jarrow-Morton framework Under the Heath-Jarrow-Morton (HJM) framework the dynamics of the Ho-Lee short rate model are defined as following: $$dr (t)=\theta (t)dt+\sigma dW^ {\mathbb {Q}} (t)$$ with $\mathbb {Q}$ the risk-neutral measure (not real world)
forward rate - Markov property in HJM model and Vasicek model . . . 1 The Vasicek model is Markovian because the stochastic differential equation of short rate r is only dependent on state t, dr (t) = k (θ-r (t))dt +σdW (t) 2 "Markov Representation of the Heath-Jarrow-Morton Model", Cheyette 1992 I am not following exactly but it says with the separable specification we could derive Markovian state variables