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.