Implied volatility (IV)

简要解答

Implied volatility is the annualized amount of movement in a stock that option prices currently imply. It is not observed directly; it is the volatility number that, when fed into an option pricing model, reproduces the price an option actually trades at. In that sense it is the option market's collective estimate of how much the stock might move — in either direction — over the life of the option.

Higher IV means options cost more, because larger expected swings make both calls and puts more likely to finish with value. IV says nothing about direction, only magnitude.

Options Band summarizes each stock's option market with IV30, a 30-day interpolated at-the-money figure described at the IV30 methodology page.

深入了解

IV is quoted as an annualized standard deviation. To translate it into a horizon that matches an option, scale it by the square root of time: a T-day standard deviation equals the annual figure times the square root of T/365.

A worked example with round numbers:

• Stock price: $100
• IV30: 30% (annualized)
• Horizon: 30 days

The scaling factor is √(30/365) ≈ 0.29, so the implied one-standard-deviation move is 30% × 0.29 ≈ 8.7%, or about $8.70 on a $100 stock. If the option market's estimate were exactly right and returns were roughly normal, the stock would finish between about $91.30 and $108.70 two-thirds of the time, and outside that range the other third. The same arithmetic underlies the expected move calculation.

Two practical notes. First, IV moves constantly: it tends to rise when demand for options builds — often ahead of earnings or amid broader uncertainty — and to fall when the uncertainty resolves. Second, a stock does not have one IV. Every strike and every expiration carries its own, which is why summary figures such as IV30 exist, and why skew and term structure are separate subjects.

Setting IV beside realized volatility shows whether the option market is pricing more or less movement than the stock has recently delivered — a descriptive comparison, not a verdict on which side is right.

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Formally, implied volatility is defined relative to a pricing model, most commonly Black-Scholes: it is the volatility input that makes the model price equal the observed market price.

C(S, K, T, r, σ) = observed option price, solved for σ

Because model price is monotonic in σ, the solution is unique, but it inherits every simplification of the model — constant volatility, lognormal returns, frictionless hedging. That different strikes on the same underlying yield different σ values (the smile) is direct evidence the model serves as a quoting convention rather than a literal description of returns.

Common misconceptions: IV is not a forecast of realized volatility, though the two are related. On average, index IV has tended to sit above subsequently realized volatility — a gap known as the volatility risk premium — so equality should not be assumed in either direction. Nor is IV a probability of profit or a directional signal. Note also that Options Band's IV values are derived from Cboe delayed chain data, so intraday readings lag the live market.