How is the VIX actually calculated from option prices?

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AcadiFi · Accepted Answer

The VIX is a model-free estimate of 30-day risk-neutral variance, computed as a weighted sum of out-of-the-money SPX option prices weighted by 1/K^2.

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The weighting 1/K^2 is crucial — it comes from the replication result that a log contract (payoff = log S_T) can be statically hedged with a continuous strip of OTM options weighted by 1/K^2. Since variance = -2 * E[log(S_T/F)] under log-normal-like dynamics, this strip replicates a variance swap.

A worked mechanic: suppose Brightwater Exchange builds a VIX-like index on a small-cap ETF. They collect 40 OTM put strikes and 40 OTM call strikes at the two nearest monthly expiries, drop any option with a zero bid, and truncate when two consecutive zero bids appear. They interpolate between the near-term and next-term expiries to hit the constant 30-day horizon. The result is annualized by multiplying by sqrt(365/30). Key FRM exam points: VIX is model-free (no Black-Scholes assumption), it captures the whole skew not just ATM, and it equals sqrt(variance swap rate) up to a small convexity term. The 2008 methodology change moved from 8 near-ATM options to the full OTM strip.

How is the VIX actually calculated from option prices?

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