简要解答

A stock's options do not share one implied volatility across time. Each expiration carries its own at-the-money IV, and plotting those against days-to-expiration traces the term structure — the volatility curve through time, sibling to the skew across strikes.

In quiet conditions the curve usually slopes gently upward: distant expirations carry slightly higher IV, since more can happen in six months than in six days. The shape inverts when something imminent looms — an earnings date, a ruling, a product decision — lifting near expirations well above far ones.

Options Band's IV30 is read off this curve, interpolating between the expirations that bracket 30 days; the method is described at /methodology/iv30.

深入了解

Because variance — volatility squared — is what accumulates over time, interpolation along the curve is done in variance terms rather than by averaging vol numbers directly. A worked example of the IV30-style calculation with round numbers:

• Near expiration: 20 days out, ATM IV 28%
• Far expiration: 40 days out, ATM IV 32%
• Target horizon: 30 days

Convert each IV to total variance: 0.28² × 20/365 ≈ 0.0043 and 0.32² × 40/365 ≈ 0.0112. Thirty days sits halfway between the two expirations, so interpolate to roughly 0.0078, re-annualize by multiplying by 365/30, and take the square root: about 30.7%. That lands slightly above the naive 30% average of the two IVs because variance weighting gives the higher, longer-dated reading more pull.

The curve's shape is informative in itself. A hump at one expiration flags an event priced inside that window and not before it; a steeply inverted front end says the market expects near-term turbulence to subside. Once the event passes, the front of the curve typically collapses toward the rest — the mechanics behind the post-earnings IV drop discussed under earnings volatility.

Reading the term structure alongside a summary number matters because IV30 can be identical for two stocks whose curves look nothing alike: one flat and calm, the other carrying a violent front-month bump that the interpolation averages away.

正式说明

The natural object is total implied variance, w(T) = σ(T)² × T. Static no-arbitrage requires w(T) to be non-decreasing in T at fixed moneyness; a violation would admit a calendar arbitrage. Forward variance between two expirations follows from the same quantity:

σ_fwd² = (σ₂² × T₂ − σ₁² × T₁) ÷ (T₂ − T₁)

An inverted spot curve can therefore still be internally consistent, provided total variance keeps rising with maturity. Forward variance is also the standard way to isolate an event: given expirations before and after it, the variance attributable to the event window is the difference in total variance — a calculation related to the expected move around earnings.

Limitations and misconceptions: the ATM term structure is one slice of a two-dimensional surface, and "the" curve depends on the moneyness convention used to define ATM at each tenor. An upward slope is not a forecast that volatility will rise — long-dated IV embeds both an expectation and a risk premium. And interpolated points such as IV30 are constructions, sensitive to which listed expirations bracket the target date and to how liquid those chains are.