A Non-Structural Investigation of VIX Risk Neutral Density

We propose a non-structural method to retrieve the risk-neutral density (RND) impliedby options on the CBOE Volatility Index (VIX). The methodology is based on orthogonalpolynomial expansions around a kernel density and yields the RND of the underlyingasset without the need for a parametric specification. The classic family of Laguerre expansionsis extended to include the GIG and the generalized Weibull kernels. We showthat orthogonal polynomial expansions yield accurate approximations of the RND of VIXand, in some cases, they outperform commonly used non-parametric methods. Based ona panel of observed VIX options, we retrieve the variance swap term structure, the timeseries of VVIX, the VIX risk-neutral moments and the Volatility-at-Risk, which reveal anumber of stylized facts on the RND of VIX