Forward volatility
Forward volatility is the implied volatility for a future period between two expiries, extracted from the implied volatilities of those two expiries. Because variance adds over time, it isolates what the options market prices for that window alone, which is how an event between two expiries shows up in the term structure.
Senzoukria · Glossary · Updated September 2026
At a glance
- Formula
- σf = √[(σ2²·T2 − σ1²·T1) / (T2 − T1)]
- Requires
- σ2²·T2 ≥ σ1²·T1, otherwise calendar arbitrage
- Use
- Isolate the volatility priced for a window between two expiries
Variance adds, volatility does not
Implied volatility is quoted per year, but what accumulates over time is variance: σ² multiplied by time. The total implied variance to the second expiry equals the variance to the first expiry plus the variance of the window between them. Solving for the window gives the forward volatility formula. It is the volatility a trader locks in by buying the longer option and selling the shorter one in the right proportion, which is why calendar spreads are described as trades on forward volatility.
Worked examples
A 7-day option is quoted at 18% and a 30-day option at 15%. The forward volatility from day 7 to day 30 is √[(0.15² × 30 − 0.18² × 7)/23] = 13.96%: the market prices the later window below both spot volatilities, because the front is elevated.
Now a 5-day option at 14% and a 12-day option at 22%, with a scheduled announcement between the two expiries. The forward volatility for days 5 to 12 is √[(0.22² × 12 − 0.14² × 5)/7] = 26.3%, far above either figure. The window containing the event is where the market places its extra variance.
What to watch
- If the formula's numerator is negative, total variance decreases with maturity, which is a calendar arbitrage or a data problem.
- Use consistent time units, calendar or trading days, and the exact time to each expiry for short-dated options.
- A humped term structure, with one expiry above both neighbours, is the visible sign of a large forward volatility in the window just before that expiry.
- Forward volatility is a price, not a forecast: it includes whatever risk premium sellers demand for that window.
In Senzoukria
Senzoukria does not compute forward volatility. Its Volatility page shows the IV term structure of the loaded chain, one at-the-money implied volatility per expiry, and classifies its shape as contango, inverted, flat or humped, naming the expiry at the peak and describing a hump as one dated event priced on that expiry and not on its neighbours. Applying the formula above to two points of that curve gives the forward volatility between them.
Related
- Volatility term structure
- Volatility surface
- Implied volatility (IV)
- Volatility: smile, term structure and skew
In the same section
- Calendar spread
- Volatility crush
- Front month
- Forward test
- Funded account
- Footprint vs candlestick
- Funding rate
- Footprint software
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Frequently asked questions
- Why can forward volatility be higher than both spot volatilities?
- Because it concentrates the extra variance of a window. If an event falls between two expiries, the longer option's total variance includes it while the shorter one's does not, and dividing the difference by the short window gives a high annualised figure.
- What does a calendar spread have to do with forward volatility?
- A long calendar, long the later expiry and short the earlier one, gains if the implied volatility for the window between them rises and loses if it falls, other things equal. Its value is driven largely by the forward volatility of that window.