VIX (CBOE Volatility Index)
Quantitative Finance glossary · Derivatives Pricing & Volatility Surfaces
Definition
Model-free implied-volatility index, computed as the square root of the 30-day variance swap rate replicated from the strip of out-of-the-money S&P 500 options: VIX^2 ≈ 2/Tsum_i (Δ K_i)/(K_i^2),e^rT,Q(K_i) - 1/Tleft(F/K_0 - 1right)^2. Unlike Black-Scholes implied vol, no model assumption — only static replication via Carr-Madan. Empirically negatively correlated with SPX returns (ρ ≈ -0.7 to -0.8), hence the 'fear gauge'. VIX futures and ETPs let traders express forward variance directly.
VIX (CBOE Volatility Index) in plain English
The VIX is basically the stock market's built-in anxiety meter. It reads the prices people are paying for insurance on the S&P 500 (options that pay off if stocks move a lot) and turns that into one number: roughly how big a swing traders expect over the next 30 days. When everyone is scared, they bid up that insurance, and the VIX shoots up — which is why it's nicknamed the 'fear gauge' and tends to spike exactly when stocks are crashing. The clever part is it doesn't assume any theory about how prices move; it just adds up the actual insurance prices across many strike levels, like averaging every quote on the board to get the market's honest guess.
Also called: CBOE Volatility Index
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