A non-structural investigation of VIX risk neutral density
提出一种非结构性方法，利用正交多项式展开从VIX期权中提取风险中性密度，无需参数设定，并揭示了VIX风险中性密度的若干典型特征。
We propose a non-structural method to retrieve 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. We show that orthogonal polynomial expansions yield accurate approximations of the RND of VIX and they generally outperform commonly used non-parametric methods when controlling for accuracy. Based on a panel of observed VIX options, we retrieve the variance swap term structure, the time series of VVIX, the VIX risk-neutral moments and the Volatility-at-Risk, which reveal a number of stylized facts on the RND of VIX.