The Fine Structure of Variance: Consistent Pricing of VIX Derivatives

Abstract:     
This paper provides a tractable framework for consistently modeling and pricing the two most actively traded options on the Chicago Board Options Exchange (CBOE), namely SPX and VIX options. We derive the dynamics of the CBOE volatility index and give semi-closed form solutions for derivatives on it in a general affine jump-diffusion setup. We compare the implications of several special cases of the general model with the major empirical properties of VIX derivatives and the time-series behavior of the VIX. We show that commonly employed affine jump-diffusion models cannot reproduce the basic patterns observed in the data. The fine structure of the variance process is essential to reconcile the empirical regularities with the theoretical models. We find that both variance jumps and a stochastic volatility of variance seem to be important factors in this respect.

Number of Pages in PDF File: 45

Keywords: Jump-diffusion model, volatility derivatives, VIX options

JEL Classification: G13

working papers series