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


  • The present article is a revised version of the author's PhD thesis at the University of Queensland. The author substantially benefited from the excellent suggestions of two anonymous referees. In addition, the author thanks the PhD committee, Philip Gray and Stephen Gray, whose comments have led to significant improvements to the present article. The author is also grateful to Philip Hoang, Kevin Davis, Sirimon Treepongkaruna and seminar participants at the 2004 Accounting and Finance Association of Australia and New Zealand Conference, Alice Springs, Australia, for helpful discussions. The author thanks the Department of Education, Training and Youth Affairs, Australia, and the University of Queensland (UQ) for their respective International Postgraduate Research Scholarships (IPRS) and UQIPRS funding supports.


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.