I was recently reading (and very much struggling to understand) the CBOE white paper on their Skew Index (CBOE Link), I thought it might be useful as I'm trying to better understand volatility skews. I'm having a lot of difficulty and I was wondering if someone who understands could clarify for me.
It seems like the CBOE calculates the Skew index by calculating the price of 3 portfolios of options, that have power payoffs. Is this referring explicitly to exotic power options?
What is the actual intuition behind these portfolios? I understand the VIX somewhat, the VIX is like a variance swap and that can be statically replicated by a weighted portfolio of options that creates a constant Vega exposure which then, in a sense, tracks changes in implied volatility.
That makes sense to me intuitively, I don't understand how the CBOE skew works on that level. Can anyone please help me understand?