VEGA FIELD GUIDE · 09 · VOLATILITY
Term structure and forward volatility
An option expiration is a time window. Line up several windows and a curve appears. That curve shows where uncertainty is concentrated and gives calendar trades their shape.
The term structure compares a consistent volatility point across maturities.
Forward volatility comes from the difference in total variance between two expirations.
Calendar shape can reflect events, mean reversion, macro dates, and supply-demand pressure.
A curve made from comparable points
A useful term structure holds moneyness or delta reasonably constant while maturity changes. Vega’s headline curve uses constant-maturity ATM volatility at tenors such as 14, 30, 60, 90, and 120 calendar days. Constant maturity reduces the sawtooth caused by listed expirations rolling down one day at a time.
An upward curve means longer-dated annualized volatility is higher. An inverted curve means the front end is higher. The curve can bend around earnings, regulatory decisions, product launches, elections, or macro releases.
Total variance is the common currency
Aggregate volatility across time by first converting it to total variance. Multiply annualized variance by time to maturity in years. A longer option can have lower annualized IV and still contain more total uncertainty because it spans more days.
This relationship powers constant-maturity interpolation and forward-volatility calculations. It also supplies a useful quality check: total variance should generally avoid decreasing as maturity increases for comparable strikes under clean, arbitrage-aware inputs.
w(T) = IV(T)^2 x T, with T measured in yearsExtract the forward window
Forward volatility describes the annualized variance implied between two future dates. Subtract the shorter maturity’s total variance from the longer maturity’s total variance, divide by the length of the forward window, and take the square root.
A 30-to-60-day forward measures the market’s price for the second month. It is especially handy around a known event because the event may fall inside one forward interval and outside another.
FwdVol(T1,T2) = sqrt[(T2 x IV(T2)^2 - T1 x IV(T1)^2) / (T2 - T1)]Worked example: the second and third month
Assume 30-day ATM IV is 24% and 90-day ATM IV is 30%. The 30-to-90-day forward volatility is the square root of [(90 x 0.30² - 30 x 0.24²) / 60]. The result is about 32.6%. Day units cancel because both maturities use the same scale.
The spot curve rises six volatility points, while the forward window prices 32.6%. The market is assigning meaningfully more annualized variance to days 31 through 90 than to the first 30 days. Check the event calendar and neighboring tenors before giving the slope a narrative.
| Window | ATM IV | Total variance in day units |
|---|---|---|
| 0 to 30 days | 24.0% | 30 x 0.24² = 1.728 |
| 0 to 90 days | 30.0% | 90 x 0.30² = 8.100 |
| 30 to 90 days | 32.6% | (8.100 - 1.728) / 60 |
Research the curve before trading the calendar
- Open the symbol term-structure history and see whether today’s slope is common for the name.
- Use Surface Lab to inspect forward windows and quality labels around each node.
- Mark earnings and other known events on the exact expiration intervals they affect.
- Check skew at both expirations. A calendar spread can carry different strike exposure as spot moves.
- Model the full position through time in the calculator. Calendars have mark-dependent outcomes before the back leg expires.
A constant 30-day point often blends two listed expirations. Keep listed quotes, interpolation status, and surface quality available during review.
Follow the curve through time
View current constant-maturity tenors, their history, forward windows, and comparison symbols.