Term structure modelling and the dynamics of Australian interest rates

This thesis consists of two related parts. In the first part we conduct an empiricalexamination of the dynamics of Australian interest rates of six different maturities,covering the whole yield curve. This direct study of the long rates is quite novel. Weuse maximum likelihood estimation on a variety of models and find some results thatare in stark contrast to previous studies. We estimate Poisson-jump diffusion (PJD)models and find very strong evidence for the existence of jumps in all daily interestrate series. We find that the PJD model fits short-rate data significantly better than aBernoulli-jump diffusion model. We also estimate the CKLS model for our data andfind that the only model not rejected for all six maturities is the CEV model in starkcontrast to previous findings. Also, we find that the elasticity of variance estimate inthe CKLS model is much higher for the short-rates than for the longer rates where theestimate is only about 0.25, indicating that different dynamics seem to be at work fordifferent maturities. We also found that adding jumps to the simple diffusion modelgives a larger improvement than comes from going from the simple diffusion to theCKLS model. In the second part of the thesis we examine the Flesaker and Hughston(FH) term structure model. We derive the dynamics of the short rate under both theoriginal measure and the risk-neutral measure, and show that some criticisms of thebounds for the short rate may not be significant in actual applications. We also derivethe dynamics of bond prices in the FH model and compare them to the HJM model.We also extend the FH model by allowing the martingale to follow a jump-diffusionprocess, rather than just a diffusion process. We derive the unique change of measurethat guarantees the family of bond prices is arbitrage-free. We derive prices for capsand swaptions, and extend the results to include Bermudan swaptions and show howto price options with the jump-diffusion version of the FH model.