Vanna (which is not represented by a greek letter) is one of the options greeks which are collectively used to determine how closely an options or warrants contract will track its underlying market. Specifically, vanna is the rate at which the delta (Δ) of an options or warrants contract will change in relation to changes in the volatility of its underlying market. Vanna is also the rate at which the vega (v) of an options or warrants contract will change in relation to changes in the price of its underlying market. Vanna is a second order derivative, and is useful when a trader is making a delta or vega hedged trade.
Vanna is the second derivative of the value (V) of an options or warrants contract, with respect to the price and the volatility of the underlying market. Vanna is calculated as shown in the above calculation image. Vanna is mathematically equivalent to both the first derivative of delta with respect to volatility, and the first derivative of vega with respect to the underlying market's price.
Use In Trading
Vanna is the rate that the delta and vega of an options or warrants contract will change as the volatility and price of the underlying market change (respectively). Vanna is therefore useful for traders that want to make a delta or vega hedged trade. In other words, traders that want to make an options or warrants trade where the delta or vega do not change regardless of what happens in the underlying market, will need to use vanna.