Term structure of volatility

ATM IV, expiry by expiry

Take the at-the-money implied volatility of each listed expiry and plot it against days to expiry: that curve is the term structure. Where the smile shows how IV varies across strikes, the term structure shows how it varies across time.

Contango and backwardation

• Contango (upward slope): short-dated IV below long-dated. This is the usual state in calm markets. Near-term options price the quiet the market is seeing now; longer ones price the chance that something happens over months.
• Backwardation (inverted): short-dated IV above long-dated. It appears in stress, during a crash or right before a major event, when the market expects the next days to be wild but things to settle afterwards. It rarely lasts.

Forward volatility

Two points of the curve imply the volatility between them. Total variance (IV² × time) adds up across periods, so the forward volatility from expiry 1 to expiry 2 is √((IV₂² × t₂ − IV₁² × t₁) / (t₂ − t₁)).

• In contango with 7 days at 44%, 30 days at 50% and 90 days at 54%, the forward volatility from day 30 to day 90 is √((0.54² × 90 − 0.50² × 30) / 60) = 55.9%.
• In backwardation with 7 days at 75%, 30 days at 62% and 90 days at 55%, it is 51.1%: the market expects the storm to pass.

Total variance must grow with time; a longer expiry whose total variance is lower than a shorter one's would be a calendar arbitrage.

Event bumps

A scheduled event, an FOMC decision or a CPI release, adds its expected move to every expiry after it, and weighs most in the shortest one. If BTC normally runs at 45% and the event is worth a 5% one-day move, a 7-day expiry spanning it trades at √((0.45² × 7/365 + 0.05²) / (7/365)) = 57.7%, while a 30-day expiry only rises to 48.3%. After the event, the 7-day IV drops straight back: the volatility crush.

Calendar spreads

A long calendar sells a near expiry and buys a far one at the same strike. With BTC at $100,000, selling the 7-day $100,000 call at 44% ($2,430) and buying the 30-day one at 50% ($5,714) costs $3,283, with net vega of about +$59 and net theta of about +$78 a day. It earns as the near option decays faster, and it gains if longer-dated IV rises. The short calendar is the reverse. The slope of the term structure decides how rich each leg is: backwardation makes the near leg rich to sell, for a reason.

How BOSS shows it

For each listed expiry, BOSS takes ATM IV as the average of the at-the-money call's and put's IV. The constant 7- and 30-day figures are interpolated in total variance between the two expiries around them. The history chart sets today's curve against the hourly record closest to a week ago (the oldest one, while less than a week has been recorded; on Deribit, when no hourly record lies within a day of that mark, a day rebuilt from Deribit's historical trades stands in), leaving out expiries under a day away, whose IV swings with the last hours' noise.