This thesis focuses applications of GARCH and regime switching models to financial markets and contains four chapters. The second chapter allows different parameters in the GARCH process for different situations of volatility in financial markets. The data generating process for asset returns has a second moment that is time-varying, persistent and subject to suddent regime shifts. The third chapter identifies how regime-dependent stochastic trends in fundamentals affect the behavior of exchange rates given an exchange rate determination model. Big swings in exchange rates in the chapter are the result of stochastic trends in fundamentals if exchange rates are an endogenous variable in the economy. Finally, the fourth chapter tests the forward-looking rational expectations monetary model of exchange rate determination with present value models, in a VAR context and when the data generation process is subject to changes in regime