Topics in Financial Asset Pricing: Equity Premium Puzzle and HMM Models for Equity Market Returns

I propose a long run risk model with two shocks based on Bansal and Yaron's well-known long-run risk model, to better capture the movements of financial markets and the US economy. My model helps resolve the equity premium puzzle. The GMM(Generalized Method of Moments) method is used to estimate the unknown parameters of the model. In the second part of my thesis, two kinds of HMM segmentation are applied to the SP500 monthly data, one is "mean segmentation" and the other is "variance segmentation". In each segmentation, two- and three-state HMMs are fitted. HMM model with mean and\or transition matrix elements rely on co-variates are fitted as well. The result shows that "buying winner and selling losers" is a great strategy of trading SP500 on monthly basis. The model also suggests that the conventional motion of Bull and Bear markets may make some sense.