- Skew of VIX options is independent of underlying level
- VIX ATM IV is highly correlated with SPX skew (now that there is an index for that I would like investigate this further)
- How to properly calculate realized volatility of the VIX. The authors write that "calculating realized volatility of VIX futures is complicated because the underlying VIX futures are systematically more volatile with decreasing time to maturity" Their solution is to calculate realized volatility of the futures contract following the forecast date.
- To model VIX ATM IV they use a simple model of VIX realized volatility and SPX skew. Term structure of ATM volatility is calculated with exponential extrapolation (there are two unknown parameters - long-term vol of vol level and smoothing parameter alpha). Skew of the VIX options is linear in futures level and extrapolated to different maturities using √T
Jul 26, 2011
VIX Options Skew
I just came across an excellent piece of research by a team of Barclays quants. The document is available here. Although the main topic of the document is about hedging, there are interesting empirical observations about VIX volatility surface. The juicy stuff starts on page 10, and is summarized on page 20. Below are the main points: