  The analytical tractability of affine (short rate) models, such as the
Vasicek and the Cox-Ingersoll-Ross models, has made them a popular choice for
modelling the dynamics of interest rates. However, in order to account properly
for the dynamics of real data, these models need to exhibit time-dependent or
even stochastic parameters. This in turn breaks their tractability, and
modelling and simulating becomes an arduous task. We introduce a new class of
Heath-Jarrow-Morton (HJM) models that both fit the dynamics of real market data
and remain tractable. We call these models consistent recalibration (CRC)
models. These CRC models appear as limits of concatenations of forward rate
increments, each belonging to a Hull-White extended affine factor model with
possibly different parameters. That is, we construct HJM models from "tangent"
affine models. We develop a theory for a continuous path version of such models
and discuss their numerical implementations within the Vasicek and
Cox-Ingersoll-Ross frameworks.
