Option pricing with regime switching GARCH volatility

This thesis develops an option pricing model where the conditional volatility and mean of the underlying asset return follow a regime switching GARCH (1,1) process. This regime switching GARCH (1,1) process allows the volatility to follow GARCH (1,1) process within each regime and to switch between regimes according to a discrete homogeneous first order Markov process. Empirical analysis based on sampled S&P 500 index options shows that the regime switching GARCH (1,1) model has much smaller squared errors than the GARCH (1,1) model of Duan (1995). Test statistics from a sign test and consistency analysis with respect to log likelihood value also suggest that the regime switching GARCH (1,1) model could be considered an improvement on Duan's GARCH (1,1) model. This thesis also shows that the Black-Scholes model can be better than the regime switching GARCH (1,1) model if the input volatility is set to the quantity that could be loosely taken as the unconditional volatility of the high volatility regime.