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This article explores the relationship between the SPX and VIX optionsmarkets. High-strike VIX call options are used to hedge tail risk in the SPX,which means that SPX options are a reflection of the extreme-strike asymptoticsof VIX options, and vice versa. This relationship can be quantified usingmoment formulas in a model-free way. Comparisons are made between VIX and SPXimplied volatilities along with various examples of stochastic volatilitymodels.

Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options