Net volatility

Net volatility refers to the volatility implied by the price of an option spread trade involving two or more options. Essentially, it is the volatility at which the theoretical value of the spread trade matches the price quoted in the market.

Formula

The net volatility for a two-legged spread (with one long leg, and one short) can be estimated, to a first order approximation, by the formula:

$\sigma _{N}={\frac {\nu _{L}\sigma _{L}-\nu _{S}\sigma _{S}}{\nu _{L}-\nu _{S}}}\,$

where

$\sigma _{N}$ is the net volatility for the spread

$\sigma _{L}$ and $\nu _{L}$ are the implied volatility and vega for the long leg

$\sigma _{S}$ and $\nu _{S}$ are the implied volatility and vega for the short leg

Example

You are considering going long a Sep/May 100 call spread, i.e. buy the Sep 100 call and sell the May 100 call. The Sep 100 call is offered at a 14.1 implied volatility and the May 100 call is bid at a 18.3 implied volatility. The vega of the Sep 100 call is 4.3 and the vega of the May 100 call is 2.3. Using the formula above, the net volatility of the spread is:

${\frac {14.3\%\cdot 4.3-18.1\%\cdot 2.3}{4.3-2.3}}=9.9\%\,$