Estimating short rate models with application to bonds and bond options

• Published: 2014
• Subjects: Interest rates - South Africa - Statistics
• Online Access: http://hdl.handle.net/10210/8785

M.Sc. (Mathematical Statistics) === In this dissertation we investigate the South-African interest rate market by analyzing the Johannesburg Interbank Agreed rate (JIBAR) and the South-African three-month treasurybill rate. In particular, we assess the goodness-of-fit of some well known parametric singlefactor short rate models. In all the data sets investigated, we firstly found the interest rate increments to exhibit severe nonnormalities, which is also found to be the case in numerous other empirical studies. Secondly, we reject the model fit for the various parametric short rate models tested. Thirdly, we found strong evidence to support the presence of jumps in all the data sets and that interest rate increments mostly exhibit fat-tailed distributions. Consequently, we tested the ability of diffusion models, driven by Brownian motions, to generate jump induced nonnormalities via a nonparametric test of diffusion model fit. The nonparametric short rate model was rejected, i.e diffusion models are misspecified. Lastly, since diffusion models are misspecified we investigated whether a jump-diffusion model can be fitted to the data with higher accuracy. In conclusion we find that a jump-diffusion model, namely the Vasiˇcek jump-diffusion model, can adequately generate the jump induced nonnormalities present in each of the data sets.