An option sensitivity (literally a cross Greek) that measures the rate of change of vega in one underlying in reaction to a change (say, 1%) in the level of another underlying. Mathematically, cross vanna is given by:

where: c is the option’s value (a call value), S₁ is the price/rate of the first underlying, S₂ is the price of the second underlying, σ₁ is the standard deviation of the first underlying, and σ₂ is the standard deviation of the second underlying.

Differently stated, cross vanna measures the rate of change of delta in the second underlying in response to a change in the volatility of the first underlying. Like other cross Greeks, cross vanna is used by traders to calculate the sensitivity for options on two underlyings.