A dimension‐invariant cascade model for VIX futures

Abstract

We propose a new stochastic volatility model by allowing for a cascading structure of volatility components. The model, under a minor assumption, allows us to add as many components as desired with no additional parameters, effectively defeating the curse of dimensionality often encountered in traditional models. We derive a semi‐closed‐form solution to the VIX futures price, and find that our six‐factor model with only six parameters can closely fit spot VIX and VIX futures prices from 2004 to 2015 and produce out‐of‐sample pricing errors of magnitudes similar to those of in‐sample errors.