Explosion in the quasi-Gaussian HJM model (Q1650943)

The authors study the explosion of the solutions of the stochastic differential equations (SDE) in the quasi-Gaussian Heath-Jarrow-Morton (HJM) model with constant elasticity of variance (CEV) model for the volatility dependence on the short rate. It is known that the quasi-Gaussian HJM models provides an efficient approach for modeling the dynamics of the yield curve. This matter follows from the low-dimensional Markovian (realisation) representation which simplifies their numerical implementation and simulation. It is rigorously shown that the short rate in these models explodes in finite time with a positive probability, under certain assumptions for the model parameters, and that the explosion occurs in a finite time almost surely under some stronger assumptions. The results are applied for the pricing of zero coupon bonds and Eurodollar futures under the model considered in the paper.