Reading an implied volatility term structure
Why longer-dated options usually imply more volatility, what makes a curve invert, and why total variance is the right thing to interpolate.
The term structure is the at-the-money implied volatility of each listed expiration plotted against time to expiration. It usually slopes gently upward and inverts when the market prices a dated event inside the front expiration.
The usual shape
A longer horizon admits more uncertainty, so at-the-money implied volatility normally rises with time to expiration. The slope is gentle: a ratio of the 90-day reading to the 30-day reading typically sits a few percent above one.
This site reports that ratio directly as the term-structure slope. A ratio rather than a difference, so a calm name and a volatile one with the same shape produce the same number and can be compared.
What inverts it
An expiration that captures a scheduled announcement carries the variance of that event on top of ordinary trading. Because the event contributes a fixed amount of variance regardless of tenor, its effect on annualised volatility is largest for the shortest contract that contains it.
The result is an inverted front: a two-week expiration printing a higher implied volatility than a three-month one. The curve reverts once the event has passed and the variance is realised.
Interpolating between expirations
Constant maturities such as the 30-day and 90-day readings are interpolated between the two listed expirations that bracket them. The interpolation happens in total variance — volatility squared, times time — and is linear in time.
Interpolating volatility directly instead is the common shortcut and it produces term structures that admit an arbitrage: between two expirations it can imply a negative forward variance, which is a claim that a longer option is worth less than a shorter one at the same strike. A tenor beyond the longest listed expiration is reported as unavailable rather than extrapolated.