A Non-Structural Investigation of VIX Risk Neutral Density

We propose a non-structural pricing method to derive the risk-neutral density (RND) implied by options on the CBOE Volatility Index (VIX). The methodology is based on orthogonal polynomial expansions around a kernel density and yields the RND of the underlying asset without the need for a parametric specification. The classic family of Laguerre expansions is extended to include the GIG and the generalized Weibull kernels, thus relaxing the conditions required on the tail decay rate of the RND to ensure convergence. We show that the proposed methodology yields an accurate approximation of the RND in a large variety of cases, also when the no-arbitrage and efficient option prices are contaminated by measurement errors. Our empirical investigation, based on a panel of traded VIX options, reveals some stylized facts on the RND of VIX. We find that a common stochastic factor drives the dynamic behavior of the risk neutral moments, the probabilities of volatility tail-events are priced in the options as jumps under the risk-neutral measure, and the variance swap term structure depends on two factors, one accounting for the slope and one for the mean-reverting behavior of the VIX.