Local Volatility of Volatility for the VIX Market

Following a trend of sustained and accelerated growth, the VIXfutures and options market has become a closely followed, active andliquid market. The standard stochastic volatility models | whichfocus on the modeling of instantaneous variance | are unable to t theentire term structure of VIX futures as well as the entire VIX optionssurface. In contrast, we propose to model directly the VIX index, in amean-reverting local volatility-of-volatility model, which will provide aglobal t to the VIX market. We then show how to construct the localvolatility-of-volatility surface by adapting the ideas in Carr (2008) andAndreasen, Huge (2010) to a mean-reverting process.[...]