  In the current literature, the analytical tractability of discrete time
option pricing models is guaranteed only for rather specific types of models
and pricing kernels. We propose a very general and fully analytical option
pricing framework, encompassing a wide class of discrete time models featuring
multiple-component structure in both volatility and leverage, and a flexible
pricing kernel with multiple risk premia. Although the proposed framework is
general enough to include either GARCH-type volatility, Realized Volatility or
a combination of the two, in this paper we focus on realized volatility option
pricing models by extending the Heterogeneous Autoregressive Gamma (HARG) model
of Corsi, Fusari, La Vecchia (2012) to incorporate heterogeneous leverage
structures with multiple components, while preserving closed-form solutions for
option prices. Applying our analytically tractable asymmetric HARG model to a
large sample of S&P 500 index options, we demonstrate its superior ability to
price out-of-the-money options compared to existing benchmarks.
