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In this report on volatility from BNP Paribas,

https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true

it states on Page 10 that the SPX Convexity Spread is defined by Varswap - ATM IV. How does this work??

Also why do we care about SPX Convexity Ratio (= Varswap/ATM IV)?

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You can think of both ( difference and ratio ) indicators as some aggregated measure of difference between flat vol (ATM vol) and "total vol" than includes skew and kurtosis effects.

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