The authors estimated and tested different continuous-time short rate models for the UK. The preferred model encompasses both the `level effect' of Chan, Karolyi, Longstaff and Sanders (1992a) and the conditional heteroskedasticity effect of Generalized Autoregressive Conditional Heteroskedastic (GARCH) type models. The findings suggest that, including a GARCH effect in the specification of the conditional variance, almost halves the dependence of volatility on the rate levels. The paper finds weak evidence of mean-reversion and volatility asymmetries in the stochastic behavior of rates. Extensive diagnostic tests suggest that the Constant Elasticity of Variance model of Cox (1975), with an added GARCH effect, provides a reliable description of short rate dynamics. The authors demonstrate that the most important feature in short rate modeling is the correct specification of the conditional variance of changes in rates, suggesting that the conditional mean characterization is of second order.
Models of the term structure of interest rates are widely used in pricing interest rate
derivatives and instruments with embedded options, such as callable bonds and
mortgage-backed securities. Many such models are based on the simplifying assumption
that changes in the entire term structure are driven by changes in a single underlying
random factor, often taken to be the ‘short’ or ‘instantaneous’ rate of interest. Therefore,
these term structure models are called ‘Single-Factor Models’.
In this study, we provide an analysis of the short-term interest rate in the UK over a
period 20 years. The study’s contribution is to add to the literature in this area by
examining different proposed single-factor models and extending them in order to capture
time-varying volatility dynamics. We provide the first application of a time-varying
volatility version of Nowman (1997) exact discrete model, and compare it with the
extended version of the Chan et al. (1992a, hereafter CKLS) discrete approximation,
proposed by Brenner et al. (1996, hereafter BHK). The study compares the performance of
the various models using an extended set of diagnostic and prediction tests, both
in-sample and out-of-sample. |
