Neil D. Pearson
Associate Professor
Department of Finance
University of Illinois at Urbana-Champaign
Anjun Zhou
Assistant Professor
School of Management
SUNY Binghamton
Abstract
Heath, Jarrow, and Morton (1992) present a general framework for modeling
the term structure of interest rates which nests most other models as special
cases. In their framework, the dynamics of the term structure and the prices
of derivative instruments depend only upon the initial term structure and
the forward rate volatility functions. Despite their importance, there
has been little empirical work studying the forward rate volatility functions.
This paper begins to fill this gap by estimating some nonparametric models
of the forward rate volatilities. In a univariate model, the form of the
forward rate volatility function differs for different maturities, and
for some maturities appears not to be a monotonic function of the level
of the forward rate. In a bivariate model, a measure of the “slope” of
the term structure seems to have an important impact on the volatility.
These results differ from the simple models that have been proposed and
used in the literature.