Modelling conditional heteroscedasticity and jumps in Australian short-term interest rates

The present paper explores a class of jump–diffusion models for the Australian short‐term interest rate. The proposed general model incorporates linear mean‐reverting drift, time‐varying volatility in the form of LEVELS (sensitivity of the volatility to the levels of the short‐rates) and generalized autoregressive conditional heteroscedasticity (GARCH), as well as jumps, to match the salient features of the short‐rate dynamics. Maximum likelihood estimation reveals that pure diffusion models that ignore the jump factor are mis‐specified in the sense that they imply a spuriously high speed of mean‐reversion in the level of short‐rate changes as well as a spuriously high degree of persistence in volatility. Once the jump factor is incorporated, the jump models that can also capture the GARCH‐induced volatility produce reasonable estimates of the speed of mean reversion. The introduction of the jump factor also yields reasonable estimates of the GARCH parameters. Overall, the LEVELS–GARCH–JUMP model fits the data best.     

On the robustness of short–term interest rate models

This paper investigates the robustness of a range of short–term interest rate models. We examine the robustness of these models over different data sets, time periods, sampling frequencies, and estimation techniques. We examine a range of popular one–factor models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that parameter estimates are highly sensitive to all of these factors in the eight countries that we examine. Since parameter estimates are not robust, these models should be used with caution in practice.     

International linkages and macroeconomic news effects on interest rate volatility — Australia and the US

We examine international linkages between daily time series of US and Australian 3-month treasury bills and 10-year government bonds from 1987–1995, paying particular attention to the effects of macroeconomic announcements in both countries. The two countries' interest rate data are modeled by a bivariate exponential generalized autoregressive conditional heteroscedasticity (EGARCH) formulation. The results suggest that market participants believed the Reserve Bank of Australia targeted the consumer price index (CPI), while the Federal Reserve targeted economic activity. Monetary policy announcements had significant effects on interest rates, as well as on their volatility in the short term. US macroeconomic activity announcements significantly moved Australian interest rates, particularly at the short end. Australian interest rates moved significantly in response to the previous day's US interest rate shocks. The conditional volatility of the Australian interest rate changes was also significantly influenced by lagged US interest rate shocks, as well as by surprises in US macroeconomic announcements. Some macroeconomic news announcements raised conditional volatilities, while others reduced them. Overall, there was a remarkable and complex array of linkages between the two countries.     

Nonlinear Drift And Stochastic Volatility: An Empirical Investigation Of Short-Term Interest Rate Models

In this article I provide new evidence on the role of nonlinear drift and stochastic volatility in interest rate modeling. I compare various model specifications for the short‐term interest rate using the data from five countries. I find that modeling the stochastic volatility in the short rate is far more important than specifying the shape of the drift function. The empirical support for nonlinear drift is weak with or without the stochastic volatility factor. Although a linear drift stochastic volatility model fits the international data well, I find that the level effect differs across countries.     

Habit Formation and Macroeconomic Models of the Term Structure of Interest Rates

This paper introduces a new class of nonaffine models of the term structure of interest rates that is supported by an economy with habit formation. Distinguishing features of the model are that the interest rate dynamics are nonlinear, interest rates depend on lagged monetary and consumption shocks, and the price of risk is not a constant multiple of interest rate volatility. We find that habit persistence can help reproduce the nonlinearity of the spot rate process, the documented deviations from the expectations hypothesis, the persistence of the conditional volatility of interest rates, and the lead‐lag relationship between interest rates and monetary aggregates.     

REGIME-SWITCHING IN AUSTRALIAN SHORT-TERM INTEREST RATES

This paper applies a generalized regime-switching (GRS) model of the short-term interest rate to Australian data. The model allows the short rate to exhibit both mean reversion and conditional heteroscedasticity and nests the popular generalized autoregressive conditional heteroscedasticity (GARCH) and regime-switching specifications. It is shown that empirical estimates of many popular interest rate models provide curious results which imply that innovations to the short rate process are extremely persistent, and that the short rate is potentially non-stationary. The source of these curious results, which are also present in US and European interest rates, is identified in the context of the GRS model, which is shown, via specification and forecasting tests, to capture the features of Australian short-term interest rate data better than existing models. The stochastic process of short-term interest rates in Australia is compared with evidence from the US and Europe, highlighting a number of important differences.     

Term Structure of Interest Rates with Regime Shifts

We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifications with up to three factors, are sharply rejected in the data. Our diagnostics show that only the regime shifts model can account for the well–documented violations of the expectations hypothesis, the observed conditional volatility, and the conditional correlation across yields. We find that regimes are intimately related to business cycles.     

Is long memory necessary? An empirical investigation of nonnegative interest rate processes

This paper analyzes a class of nonnegative processes for the short-term interest rate. The dynamics of interest rates and yields are driven by the dynamics of the conditional volatility of the pricing kernel. We study Markovian interest rate processes as well as more general non-Markovian processes that display “short” and “long” memory. These processes also display heteroskedasticity patterns that are more general than those of existing models. We find that deviations from the Markovian structure significantly improve the empirical performance of the model. Certain aspects of the long memory effect can be captured with a (less parsimonious) short memory parameterization, but a simulation experiment suggests that the implied term structures corresponding to the estimated long- and short-memory specifications are very different. We also find that the choice of proxy for the short rate affects the estimates of heteroskedasticity patterns.     

Identifying the dynamics of real interest rates and inflation: evidence using survey data

In the context of an equilibrium asset-pricing model, the dynamicsof the instantaneous real interest rate and the instantaneousrate of expected inflation are estimated. Unlike previous models,we allow real interest rates and inflation to be mutually dependentprocesses. The model is estimated as a state-space system thatincludes observations on various maturity Treasury bills andNBER-ASA survey forecasts of inflation. Over the period 1968-1988,we find evidence that instantaneous real interest rates andexpected inflation are significantly negatively correlated.Real interest rates also display greater volatility and weakermean reversion than expected inflation.     

Additional evidence on transparency and bank financial performance

This paper examines the relationship between volatility and the probability of occurrence of expected extreme returns in the Canadian market. Four measures of volatility are examined: implied volatility from firm option prices, conditional volatility calculated using an EGARCH model, idiosyncratic volatility, and expected shortfall. A significantly positive relationship is observed between a firm's idiosyncratic volatility and the probability of occurrence of an extreme return in the subsequent month for firms. A 10% increase in idiosyncratic volatility in a given month is associated with the probability of an extreme shock in the subsequent month (top or bottom 1.5% of the returns distribution) of 26.4%. Other firm characteristics, including firm age, price, volume and book‐to‐market ratio, are also shown to be significantly related to subsequent firm extreme returns. The effects of conditional and implied volatility are mixed. The E‐GARCH and expected shortfall measures of conditional volatility are consistent with mean reversion: high short term realizations of conditional volatility foreshadow a lower probability of extreme returns.