Interest rate model theory with reference to the South African market

An overview of modern and historical interest rate model theory is given with thespecific aim of derivative pricing. A variety of stochastic interest rate models arediscussed within a South African market context. The various models arecompared with respect to characteristics such as mean reversion, positivity ofinterest rates, the volatility structures they can represent, the yield curve shapesthey can represent and weather analytical bond and derivative prices can be found.The distribution of the interest rates implied by some of these models is also foundunder various measures. The calibration of these models also receives attentionwith respect to instruments available in the South African market. Problemsassociated with the calibration of the modern models are also discussed.