VIX computation based on affine stochastic volatility models in discrete time

We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, capture the time-varying higher moments observed in financial series. Three desirable results are obtained. First, we have a recursive procedure for the log-price characteristic function which allows a semi-analytical formula for option prices as in Heston and Nandi (Rev Financ Stud 13(3):585–625, 2000). Second, we reproduce some features of the VIX Index. Finally, we derive a simple formula for the VIX index and use it for option pricing.