This thesis estimates a quadratic pricing kernel developed by Christoffersen, Heston and Jacobs (2013) under the Heston-Nandi GARCH pricing model, using both American and Canadian data. Initially, we find a misfit of data across different data samples, indicating lack of support in the closed-form quadratic pricing kernel. Comparing with the estimation of the continuous-time Heston (1993) model from Christoffersen, Jacobs, and Mimouni (2010), this empirical puzzle exists in both the Heston-Nandi (2000) GARCH and Heston (1993) stochastic volatility model.

We provide additional tests by comparing the Heston-Nandi and CHJ model with the overreaction tests. We find that their empirical performances are not differentiated. Also, we introduce the stochastic dominance bounds in order to select the mispriced options. The results from filtered data sample indicate the mispricing of options is significantly affecting the estimation.