
doi: 10.2139/ssrn.2030292
Regardless its legacy name as a volatility index, VIX is calculated as a variance swap. Unlike an actual swap, variance swap is a forward contract on realized variance. The note provides a link between theoretical pricing of a variance swap and VIX calculation formula. Pricing of a variance swap is model-independent and based on a replicating strategy using a portfolio of an infinite strip of out of the money European calls and puts. VIX calculation formula, as outlined in The VIX White Paper (CBOE, 2009), is a discretization of the theoretical pricing result.
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