In plain language — A comparable coordinate, such as forward ATM, is selected and the implied volatility associated with each expiry is observed at the same moment. The resulting line separates near-term from longer-term risk, but it does not say with certainty what will happen.
The implied volatility term structure organizes IV along the remaining life of options. The horizontal axis contains expiries or tenors; the vertical axis contains an annualized IV measure. A compact definition is:
TS(T_i; t₀, m*) = σ_imp(t₀, T_i, m*)
t₀ is the common timestamp, T_i the expiry and m* the coordinate kept
consistent: moneyness, log-moneyness, delta or another stated convention.
Without these coordinates, joining numbers labelled only “IV” may combine
economically different options.
A slice of the surface, not a universal curve
Each expiry contains many strikes. The term structure is therefore a slice of the volatility surface, not an object independent of its selection rules. Some views use the ATM option; others compare 50-delta, 25-delta put or constant log-moneyness. Two platforms can display different curves because they use different coordinates, forwards, models or filters.
“ATM” itself needs a definition. The strike nearest spot is not necessarily the strike nearest the forward, particularly when rates, dividends, carry or long maturities matter. A 50-delta coordinate depends on the model and the volatility entered in its calculation. The convention must travel with the data.
A structure observed at 10:00 a.m. is a snapshot. Repeating the same procedure each day creates a time series of snapshots, but today's curve is not itself a time series. Comparing today's 30-day point with an option that has 29 days remaining tomorrow also introduces the passage of time and a possible change in the selected contract.
Volatility level and total variance
Annualized IVs are not additive across expiries. A useful coordinate is implied total variance:
w(T) = σ_imp(T)² × T
where T is expressed in years under a stated day-count convention. Under
consistent assumptions, average forward variance between T₁ and T₂ can be
derived as:
v_forward(T₁,T₂) = [w(T₂) − w(T₁)] / (T₂ − T₁)
σ_forward = sqrt(v_forward)
This transformation helps prevent a lower IV at a longer expiry from being read as “less total uncertainty”. A lower annualized level can still correspond to greater total variance because it spans more time.
Neutral example
At the same instant, 50-delta options show:
| Days to expiry | Annualized IV | Approximate total variance |
|---|---|---|
| 21 | 32.0% | 0.32² × 21/365 ≈ 0.0059 |
| 63 | 24.0% | 0.24² × 63/365 ≈ 0.0099 |
The segment slopes down in IV levels, but total variance rises. Under the
formula's assumptions, average forward volatility between day 21 and day 63
is approximately 18.8% annualized. This is not a guaranteed forecast of RV
over that interval: it is a quantity implied by the selected prices, model and
coordinates.
If total variance falls materially with maturity, quotes, bid-ask, timestamps, parity, exercise style, dividends and interpolated strikes should be checked before concluding that an arbitrage exists.
Shapes of the structure
A curve may be:
- upward-sloping, with higher IV at more distant expiries;
- downward-sloping or inverted, with IV concentrated at the front end;
- humped, when one or more expiries contain a local discontinuity;
- irregular, because of sparse quotes, wide spreads or non-homogeneous contracts.
The terms contango and backwardation are sometimes extended informally to volatility. Saying upward-sloping, downward-sloping or inverted and naming the measure is more precise. The futures curve connects prices of futures contracts; an IV term structure connects option-implied parameters. Even the VIX futures curve is not the same object as the term structure of SPX IV: the underlying, payoff and convergence dynamics differ.
An expiry that contains an economic release, a corporate decision or another known event may show a bump. The bump indicates that prices assign value to uncertainty over that interval; it does not reveal a certain direction, outcome or realized magnitude. When several events fall within the same option, IV aggregates the remaining period and does not label each source of risk separately.
Data, interpolation and constant maturity
Quoted expiries are discrete. A “constant 30-day” measure may require interpolation between two maturities. The procedure should operate on the appropriate quantity—often total variance—and document:
- eligible expiries and day-count calendar;
- strike or delta coordinate;
- bid, ask, mid, settlement or transaction price;
- inversion model and carry inputs;
- filters for missing quotes, zero bids or excessive spreads;
- interpolation rule and any extrapolation.
A smooth chart does not make the underlying points liquid. Short-dated options can have high gamma and change quickly; distant options may quote less often. Unsynchronized timestamps can create artificial bumps. Snapshot quality is as much a part of the measure as the formula.
What it can reveal
The term structure helps to:
- identify the interval in which uncertainty is most heavily priced;
- compare the same underlying through time under a fixed methodology;
- control vega exposure distributed across expiries;
- construct non-parallel scenarios instead of moving every IV by the same number of points;
- inspect the calendar risk of a multi-leg strategy.
It is not sufficient to infer the P&L of a calendar spread. The two legs have different delta, gamma, theta, vega, strike, liquidity and surface response. Even the “correct” curve move can produce a different outcome if the underlying changes or the spread is executed away from mid.
Common errors
- Mixing fixed strikes and fixed deltas without disclosing the coordinate change.
- Using quotes from different times, creating a curve that never existed at one instant.
- Treating the snapshot as a time series or as a forecast.
- Confusing the IV term structure, a futures curve and VIX futures. They are objects with different units and contracts.
- Adding or subtracting annualized IVs as though they were variances over disjoint intervals.
- Reading a bump as proof of an event outcome. Price describes uncertainty and demand, not a certain direction.
- Ignoring bid-ask and interpolation. A theoretical point may not be executable.
Checklist
- Do all points share the same underlying, timestamp and settlement method?
- Is the coordinate strike, moneyness, log-moneyness or delta?
- Does ATM mean spot, forward, 50 delta or nearest strike?
- Is the chart showing annualized IV or total variance?
- Which prices and model generate each point?
- Which intervals contain events and dividends?
- Does the view use quoted expiries or an interpolated constant maturity?
- Do spread, liquidity or stale quotes make any node fragile?
- Does the historical comparison preserve the same methodology?
Sources
- CME Group, Volatility Term Structure Tool User Guide — ATM views by expiry and comparisons between snapshots.
- Cboe, VIX Term Structure Data and Charts — a methodological example of a timestamped multi-expiry structure.
- Options Industry Council, Understanding Volatility and Options Skew — term structure, expiries and events.
- CME Group, Understanding Options: a real-world example on the impact that skew can have on an options position — IV, skew and pricing relationships.
- CME Group, Options Analytics: Greeks and Implied Volatility — data by expiry, moneyness and Greek.
- Options Industry Council, Technical Information — the derived nature of IV and volatility conventions.
- The Options Clearing Corporation, Characteristics and Risks of Standardized Options — specifications, expiry and contractual risks.