Forward Volatility

Forward volatility is the level of volatility that option prices imply for a period lying in the future, between two expiry dates. It is derived from the implied volatility of a shorter-dated and a longer-dated option on the same underlying. Because variance adds up over time, the forward figure is found from total variances:

Here $\sigma_1$ and $\sigma_2$ are the implied volatilities for expiries $T_1$ and $T_2$, measured in years. If one-month volatility is 20 percent and three-month volatility is 24 percent, the forward variance is (0.0576 × 0.25 − 0.04 × 0.0833) ÷ 0.1667 = 0.0664, and the forward volatility for months two and three is about 25.8 percent. The market is pricing more movement after the first month than during it. Traders read forward volatility from the term structure of the volatility surface, take positions on it with a calendar spread, and compare it with their own volatility forecasting.