The VIX and Future Information

In this paper, we propose an innovative VIX model which takes future market information available to the traders into account. The future information is modeled by an initially enlarged filtration in our setup. We derive an explicit representation for the anticipative VIX process and obtain the associated time dynamics. We also investigate the pricing of variance swaps under both backward- and forward-looking information. We finally deduce the optimal mean variance hedging portfolio in a financial market consisting of a bank account and a VIX futures. In order to have some benchmark model available, we introduce a non-anticipative stochastic volatility stock price model right at the beginning and infer representations for the related VIX index, the VIX futures and a VIX call option