Explosion in the quasi-Gaussian HJM model

TL;DR

This paper proves that solutions in the quasi-Gaussian HJM model with CEV volatility can explode in finite time, affecting bond pricing and highlighting limitations of the model.

Contribution

It provides a rigorous analysis of finite-time explosion of the short rate in the quasi-Gaussian HJM model with CEV volatility, a novel insight into its behavior.

Findings

Short rate explodes in finite time with positive probability.

Explosion occurs almost surely under stronger assumptions.

Implications for pricing zero coupon bonds and Eurodollar futures.

Abstract

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.