Small-noise limit of the quasi-Gaussian log-normal HJM model

TL;DR

This paper analyzes the small-noise limit of the quasi-Gaussian log-normal HJM model, revealing conditions under which the short rate and futures prices can explode to infinity in finite time, impacting model stability.

Contribution

It provides a qualitative analysis and explicit explosion criteria for the quasi-Gaussian log-normal HJM model in the small-noise limit, highlighting potential instabilities.

Findings

Short rate can explode to infinity in finite time.

Eurodollar futures prices may also explode under certain conditions.

Explicit criteria for explosion are derived.

Abstract

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 greatly simplifies their numerical implementation. We present a qualitative study of the solutions of the quasi-Gaussian log-normal HJM model. Using a small-noise deterministic limit we show that the short rate may explode to infinity in finite time. This implies the explosion of the Eurodollar futures prices in this model. We derive explicit explosion criteria under mild assumptions on the shape of the yield curve.