Markov-Switching models and resultant equity implied volatility surfaces: a South African application - Fairbrother, Mark (University of Cape Town, 2014)
Includes bibliographical references. === Standard Geometric Brownian Motion is the stock model underlying Black-Scholes famous option pricing formula. There are however numerous problems with this stock model as certain features do not follow some empirical stylised facts we see from the observation of actual asset prices. In particular, the constant parameter idea behind Geometric Brownian Motion is flawed. It is argued that information flow dictates stock price movements and information is a function macro-economic regimes shifts. As such, we propose an alternative model, one in which the parameters in the Standard Geometric Brownian Motion change according to an underlying Hidden Markov Process. This new model, termed a Markov-Switching model, is presented in extensive detail. Parameter Estimation methods, Simulation Methods and Option Pricing Theory are explored. Summary algorithms are presented so that this dissertation may be used as a good reference guide for those wishing to apply Markov-Switching Models. The model is tested by fitting the model on South African data and using the discussed option theory to create various implied volatility surfaces. The surfaces produced appear to obey some of the empirical observations and theoretical ideas around expected implied volatility surfaces, indicating that the Markov-Switching model has some value for option pricing.