VIX MODELING FOR A MARKET INSIDER

Abstract

In this paper, we extend the popular Barndorff–Nielsen–Shephard stochastic volatility model to the case of a pure-jump Ornstein–Uhlenbeck equation with non-vanishing stochastic mean-reversion level. Based on this setup, we derive representations for the squared VIX process and related VIX futures prices. Having these results at hand, we introduce an initially enlarged filtration which models the view of a VIX market insider who has knowledge about the future behavior of the stochastic mean-reversion level of the squared volatility process available. In this enlarged filtration framework, we infer an explicit representation for the anticipative VIX process and obtain the associated time dynamics. We finally investigate the pricing of variance swaps under both backward- and forward-looking information.