Mungule, Oswald Kombe2012-01-202012-01-202012-01-20http://hdl.handle.net/10539/11118The first essay formulates a dynamic rational contagion model in order to analyse the evolution of speculative bubbles. The model consists of two laws of motion: the speculative bubble and the probability of the bubble. The rst essay shows that the model has two stable equilibria and one unstable equilibrium. The dynamics of both the nonlinear speculative bubbles and the probability interact to form two stable equilibria and one unstable equilibrium which lead to ballooning and busting of the speculative bubbles. These features of speculative bubbles are driven by the speculators’s herd behaviour, the bubbles size, the speed of change, the strength of infection, and the effects of both the bubbles and the short-term interest rate on the transition probability. The second essay extracts speculative bubbles from two nancial markets: the foreign exchange and the stock markets for South Africa between 1995Q2 and 2008Q4. The second essay uses the no-arbitrage models for the exchange rate and the stock price. By invoking the rational bubbles theory and using the residuals, we compute the asset price bubbles using the expectational restriction for rational bubbles theory. Three robustness checks on the computed bubbles con rm that speculative bubbles are present in the stock price and the exchange rate. By using iii Abstract iv graphs of speculative bubbles, we show that the speculative bubbles are consistent with the existence of bubble episodes as documented in the literature. The third essay formulates a macro-model of a small-open economy in order to investigate the relative performance of optimal monetary policy rules that respond to speculative bubbles and those that do not. The model consists of two nonlinear speculative bubbles: the stock price and the exchange rate bubbles. These speculative bubbles interact with the IS curve, the Phillips curve and the asset prices. The ndings show that policy rules that respond to speculative bubbles dominate rules that do not.enStock marketForeign exchange marketMonetary policySouth AfricaThesis