  We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM
model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular
approach for modeling the dynamics of the yield curve. This is due to their low
dimensional Markovian representation which simplifies their numerical
implementation and simulation. We show rigorously that the short rate in these
models explodes in finite time with positive probability, under certain
assumptions for the model parameters, and that the explosion occurs in finite
time with probability one under some stronger assumptions. We discuss the
implications of these results for the pricing of the zero coupon bonds and
Eurodollar futures under this model.
