We provide a new method to derive the state price density per unit probabilitybased on option prices and GARCH model. We derive the risk neutraldistribution using the result in Breeden and Litzenberger (1978) and thehistorical density adapting the GARCH model of Barone-Adesi, Engle, andMancini...

We study a new class of three-factor affine option pricing models with interdependent volatilitydynamics and a stochastic skewness component unrelated to volatility shocks. Theseproperties are useful in order (i) to model a term structure of implied volatility skews moreconsistent with the data...