Unifying Gaussian dynamic term structure models from a Heath–Jarrow–Morton perspective

Abstract

In this paper, we show that most existing Gaussian dynamic term structure models (GDTSMs) can be nested as special cases under a unified Heath–Jarrow–Morton (HJM)-based framework of GDTSM construction. Our study provides not only a systematic way to examine the commonality of many seemingly distinct GDTSMs, but also a novel and convenient approach to constructing GDTSMs that are otherwise unavailable or intractable under the traditional approach. In our empirical study using the Euro area forward rates, we conduct a specification analysis based on this novel approach. The analysis reveals that the traditional models impose restrictive constraints limiting their flexibility in capturing key features of the correlations and volatilities of the forward rates.