Implied Volatility Term Structure: Compare Expirations Correctly
For educational purposes only; not investment advice.
Direct answer
Section titled “Direct answer”The implied volatility term structure is the relationship between option-implied volatility and expiration for one underlying at one observation time. A clean comparison holds moneyness approximately constant, such as at-the-money options or a fixed Delta, then plots IV against days to expiration.
An upward-sloping curve has lower short-dated IV and higher long-dated IV; a downward-sloping or inverted curve has higher short-dated IV. A single expiration can also form a hump when it contains earnings, an economic release, an election, or another dated catalyst that the preceding expiration does not cover.
The curve is a set of risk-neutral prices shaped by expected variance, jump risk, risk premia, supply and demand, rates, dividends, and market liquidity. It is not a literal forecast that realized volatility must equal each quoted IV, and a slope alone is not an arbitrage signal.
How to measure it
Section titled “How to measure it”Use the same timestamp and comparable contracts across expirations. For equities, compare near-ATM or fixed-Delta options and account for forward price, dividends, rates, American exercise, and bid-ask quality. Comparing one expiration’s 25-Delta Put with another expiration’s ATM Call mixes skew, direction, and tenor.
Annualized IV cannot be added across time. Convert it to total implied variance:
w(T) = IV(T)² × T, where T is years to expiration.
For two maturities T₁ < T₂, the variance implied specifically between them is
forward variance(T₁,T₂) = [w(T₂) − w(T₁)] / (T₂ − T₁).
Its square root is the annualized forward volatility for that interval. This decomposition is more informative for a dated event: if the first expiration excludes earnings and the second includes it, their total-variance difference helps isolate the market price assigned to the added window. It still includes all risks in that interval, not only the named event.
Term structure and skew are different dimensions. Term structure compares expirations at matched moneyness; skew compares strikes or Deltas within one expiration. A calendar spread trades two expirations but is exposed to both curves, changing Delta, Vega, Theta, skew, and execution prices. “Sell the high IV and buy the low IV” is therefore incomplete.
Worked example
Section titled “Worked example”Suppose matched ATM IVs are:
| Days to expiration | Annualized IV | Total variance IV² × T |
Approx. one-standard-deviation move IV × √T |
|---|---|---|---|
30 |
36% |
0.01065 |
10.32% |
90 |
24% |
0.01420 |
11.92% |
180 |
22% |
0.02387 |
15.45% |
The curve is sharply inverted from 30 to 90 days, perhaps because a near-term event is priced into the first month. Yet the 90-day option contains more total variance than the 30-day option. A lower annualized IV does not mean less cumulative uncertainty over a longer horizon.
The 30-to-90-day forward variance is
(0.01420 − 0.01065) / (60/365) = 0.02159,
so annualized forward volatility is √0.02159 = 14.69%. This says the first 30 days are priced much more intensely than the following 60-day interval. It does not predict that realized volatility after day 30 will be exactly 14.69%.
If the displayed 30-day market is 35% bid / 37% ask and the 90-day market is 23% bid / 25% ask, a midpoint curve hides the executable range. A calendar trade must be tested at the package bid and ask, with the same strike/Delta convention and an explicit post-event volatility scenario.
Risk checklist
Section titled “Risk checklist”- Match moneyness, timestamp, underlying deliverable, and data methodology across expirations.
- Use current executable quotes; stale or wide markets can create false humps and inversions.
- Separate annualized IV from total variance and expected move.
- Mark earnings, dividends, FOMC decisions, court rulings, elections, and other dated events.
- Do not confuse an equity-option IV curve with the VIX futures term structure; they are different instruments and measures.
- Model both expirations after the event. Near IV can collapse while far IV, skew, and stock price also change.
- Account for different Vega, Theta, Gamma, and Delta units before sizing a calendar or diagonal.
- Include early exercise, assignment, settlement, multiplier, and pin risk.
- Treat forward variance as an implied price under risk-neutral valuation, not an unbiased realized-volatility forecast.
- Stress bid-ask widening and the possibility that only one leg fills.
Common misconceptions
Section titled “Common misconceptions”- “The highest IV expiration is the most expensive.” Expensiveness requires a benchmark, consistent moneyness, total variance, and executable prices.
- “Upward slope always means calm; inversion always predicts a crash.” Events and temporary demand can reshape a curve without that outcome.
- “Two 20% IV maturities contain the same risk.” The longer maturity contains more total variance because
Tis larger. - “A calendar spread is pure term-structure arbitrage.” It also carries path-dependent Greeks, skew, direction, assignment, and execution risk.
- “Forward volatility is the market’s exact forecast.” It includes risk premia and is inferred from option prices under assumptions.
- “The curve can be read from last trades.” Trades can be stale, at different times, strikes, or sides of the market.