Skew is the price of volatility across strikes. Term structure is the price of volatility across time. Take the at-the-money IV of every listed expiration and line them up from the nearest to the furthest. The line you get is the term structure, and its shape tells you what the market expects volatility to do from here.
The normal shape
In a calm market the line slopes upward. A 10-day option might imply 14%, a 3-month option 17% and a 1-year option 19%. That is not a forecast that the stock will get wilder. Volatility drifts back toward its long-run average, so when today's level is low the market expects more of it later on, and longer-dated options also carry a premium for everything nobody can see yet. Traders call the upward shape contango, a word borrowed from the futures markets.
ATM implied volatility by days to expiry, with the front at 14% and the long-run level at 20%. The front sits low and the curve climbs toward the long-run level. Drag the front slider above the long-run level and watch the same curve invert.
The inverted shape
When something is happening now, the line flips. In a sell-off the front expiration might jump to 35% while the 1-year sits at 24%. The market is saying that the next few weeks are the dangerous part and that things should settle after. That is an inverted curve, also called backwardation. A scheduled event does the same thing to one expiration in particular; the next lesson is about that.
The front at 40% against a long-run 24%. Move the front slider 10 points either way and see how little the far end moves: the shock lives in the first few months.
The front moves most
Short-dated IV reacts far more than long-dated IV, in both directions. A shock that adds 10 points to a 2-week option might add 2 or 3 to the 3-month and barely touch the 1-year. The reason is averaging. An option's IV is the average level of volatility it expects over its whole life. A 1-year option's life is mostly the months after the scare, when volatility is expected to be back near normal, so a bad fortnight is a small slice of its average. It cuts the other way too. When the scare passes, the front collapses first. If you own short-dated options because their IV looked high, this is the number that hurts you.
That averaging has a useful consequence. If the 1-month IV is the average of the next month and the 3-month IV is the average of the next three, then the two together tell you what the market expects for months two and three on their own. That is called the forward volatility, and it is how a trader asks whether a later expiration is cheap or dear against the one before it.
Reading the curve
Two numbers summarize the shape. The slope is the back ATM IV minus the front ATM IV, in points; positive means upward. The front-to-back ratio is the front ATM IV divided by the back. With the front at 18% and a three-month expiration at 22%, the slope is +4 points and the ratio is 0.82. A ratio under 1 is the normal state. Above 1 the curve is inverted and something is priced into the front. Calendar spreads, which sell one expiration and buy another, live and die on this ratio, so you want it in front of you before you price a single leg.
The maths: variance adds up over time
Volatility does not add across time, but variance does. The quantity that adds is total variance, w = v² × T: the IV squared times the years to expiry. The total variance to the 3-month date is the variance to the 1-month date plus the variance between the two. Solve for the part in between and you get the forward volatility: v_fwd = √[(v2² T2 - v1² T1) / (T2 - T1)].
Worked example, with the curve from the last section: 30 days at 18% and 90 days at 22%. Then v1² T1 = 0.0324 × 30/365 = 0.00266 and v2² T2 = 0.0484 × 90/365 = 0.01193. The difference, 0.00927, spread over the 60 days between, 60/365 = 0.164, is 0.0564, and its square root is about 23.7%. So a curve running from 18% to 22% is really pricing 18% for the first month and nearly 24% for the two months after it. The later months are dearer than the back number suggests. If the formula ever needs the square root of a negative number, the curve is falling faster than averaging allows, which is an arbitrage the market does not leave lying around for long.
The charts here draw the curve as a long-run level plus a front gap that shrinks by the same fraction every day, to about a third of its size every 60 days: v(d) = v_long + (v_front - v_long) × e^(-d/60). A 10-point front shock is worth about 8 points at 14 days, about 2 at 90 days and almost nothing at a year.
Your turn
Open the MSFT chain on the front expiration the first task names and read the at-the-money IV. Switch to the later monthly and do it again. Then look at Vol Snapshot's Term structure panel and check which way the line runs between those two points.