In this thesis we empirically study the pricing kernel implicit in option prices. The model is complete with a transition density model and a specification of the pricing kernel. With S&P 500 index and options data we systematically evaluate the relative importance and robustness of factor dynamics and non-linearities in the pricing kernel using various in- and out-of-sample measures. We construct the model in two stages. In the first stage we use a flexible semiparametric time-series model to describe the factor dynamics. In the second stage, we infer for each date in the sample the pricing kernel from the option prices using conditional moments implied by the restriction of no-arbitrage.;Based on the cross-sectional fits alone, we can not detect significant difference between models with different factor dynamics. This is because with sufficient free parameters any no-arbitrage model prices cross-section options by construction. Cubic pricing kernel provides almost perfect fits in the sample. Nonlinearity in the pricing kernel is crucial for in-the-sample performance. Both excess kurtosis and skewness are very important. However, a well-specified factor dynamics improves the out-of-sample pricing performance. With a well-specified factor dynamics model, the linear pricing kernel beats other competitors at 2-week horizon.
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