Options, Futures, and Other Derivatives, 10th Edition

19.8 VEGA

As mentioned in Section 19.3, when Greek letters are calculated the volatility of the asset is in practice usually set equal to its implied volatility. The Black–Scholes–Merton model assumes that the volatility of the asset underlying an option is constant. This means that the implied volatilities of all options on the asset are constant and equal to this assumed volatility.

But in practice the volatility of an asset changes over time. As a result, the value of an option is liable to change because of movements in volatility as well as because of changes in the asset price and the passage of time. The vega of an option, $\mathcal{V}$, is the rate of change in its value with respect to the volatility of the underlying asset:8

8 Vega is the name ...