Forward Volatility: Extracting a Future Window from Two Expirations

For educational purposes only; not investment advice.

Direct answer

Forward volatility is the annualized volatility implied for a future interval, such as day 30 through day 90, inferred from volatility information covering today through each endpoint. If σ1 and σ2 are consistently measured annualized volatilities for times T1 < T2, the constant-variance approximation is:

σ²forward = (σ²2T2 − σ²1T1) ÷ (T2 − T1).

The operation subtracts total variance (σ²T), not volatility percentages. The result is a market-implied, model- and quote-dependent number—not a guarantee of realized volatility and not automatically a tradable price.

Why variance is additive across time

Under the simplifying assumption that variance accumulates through non-overlapping intervals, total variance from today to T2 equals variance from today to T1 plus variance from T1 to T2. Solving for the missing interval gives the formula above. Taking the square root converts forward variance back to annualized volatility.

The inputs must describe comparable objects: same underlying, timestamp, annualization convention, and a consistent strike or moneyness treatment. A single option’s Black-Scholes IV at two unrelated strikes is not the same as a model-free expected-variance measure. Skew, jumps, dividends, rates, settlement, stale quotes, and interpolation can all change the answer. For event analysis, total variance is often more informative because a short event window can raise a near expiration sharply while adding less to a longer annualized IV.

One-month 40%, three-month 30%

Suppose comparable one-month and three-month annualized IVs are 40% and 30%. Use T1 = 1/12 and T2 = 3/12 years:

One-month total variance: 0.40² × 1/12 = 0.013333.
Three-month total variance: 0.30² × 3/12 = 0.022500.
Remaining variance: 0.022500 − 0.013333 = 0.009167.
Remaining time: 2/12 = 0.166667 year.
Forward volatility: sqrt(0.009167 ÷ 0.166667) = 23.45%.

So the market inputs imply about 23.45% annualized volatility for months two and three under these assumptions—not 30%, and certainly not 40% − 30% = 10%. The one-month number may contain a concentrated event premium. Bid/Ask inputs and a full surface calculation can produce a range rather than one precise result.

Calculation and trading checklist

Use exact year fractions and the same day-count and annualization convention.
Capture both surfaces at the same timestamp and retain Bid, Ask, strike, forward, rates, and dividends.
Compare like moneyness—preferably forward moneyness or Delta—not merely the same dollar strike.
State whether inputs are single-strike IVs, ATM interpolations, variance-swap rates, or an index methodology.
Reject or investigate negative forward variance; it often signals inconsistent quotes, interpolation, or input definitions.
Recalculate across Bid/Ask and nearby strikes to expose estimation uncertainty.
Separate an inferred metric from a position. A calendar spread also carries Delta, Gamma, Theta, skew, execution, and assignment risk.
Stress the event moving dates, being canceled, or producing a different magnitude than implied.

Common misconceptions

“Subtract the two IVs.” Variances weighted by time are subtracted.
“Forward volatility predicts what will happen.” It is an implication of current prices and assumptions.
“A high forward number identifies direction.” Volatility is primarily about dispersion, not up versus down.
“Two expirations are enough without matching strikes.” Skew makes unmatched comparisons unreliable.
“Negative forward variance is a market forecast.” It is usually a warning that inputs or methodology are inconsistent.
“A calendar spread directly trades only forward volatility.” Its actual P/L depends on the whole surface and path.