A Dimension-invariant Cascade Model for VIX Futures

Abstract

We propose a new model of volatility by allowing for a cascading structure of volatility components. The cascading feature is achieved by introducing an increasing structure to the speed of mean reversion. It allows us to add as many components as desired with no additional parameter, effectively defeating the curse of dimensionality often seen in traditional models. The flexibility in choosing the number of components enables rich dynamics in the term structure of both spot VIX and VIX futures, without the need to introduce price jumps. We derive a semi-closed form solution to the VIX futures price, and find that our 6-factor model with only 6 parameters can closely fit spot VIX and VIX futures data from 2004 to 2015 and produce out of sample pricing errors of magnitudes similar to those of in-sample errors.