Pricing Kernels with Stochastic Skewness and Volatility Risk

Online Appendix In this online appendix, I first provide a brief comparison of the small noise expansion series and the Taylor expansion series. I then use separably Taylor expansion series and the small noise expansion series to derive the pricing kernel in a one-market model with two dates, and the pricing kernel in a two-market model with three dates. I thereafter, investigate whether one obtains a pricing kernel that depends on the market co-skewness and the market volatility in a long run risk model and also in a model where the representative investor chooses his optimal allocation in the presence of the market equity and the variance swap contracts. The remaining part of the appendix contains additional tables and figures used in the paper.