The effects of asymmetric volatility and jumps on the pricing of VIX derivatives

Abstract

This paper proposes a collection of affine jump–diffusion models for the valuation of VIX derivatives. The models have two distinctive features. First, we allow for a positive correlation between changes in the VIX and its stochastic volatility to accommodate asymmetric volatility. Second, upward and downward jumps in the VIX are separately modeled to accommodate the possibility that investors react differently to good and bad surprises. Using the VIX futures and options data from July 2006 through January 2013, we find conclusive evidence for both asymmetric volatility and upward jumps in VIX derivative prices. However, we find little evidence supporting downward jumps.