Vanna is a cross-sensitivity in options pricing that measures how the delta of an option responds to changes in volatility, or equivalently how the option's Vega changes as the underlying price moves. In practice, Vanna is commonly defined as the partial derivative of Delta with respect to volatility (dDelta/dVol). It can also be viewed as the derivative of Vega with respect to the underlying price (dVega/dS). As a second-order Greek, Vanna depends on factors such as the option’s moneyness, time to expiry, interest rates, and dividend yields. Near-the-money options and longer-dated contracts tend to exhibit larger Vanna values, reflecting greater sensitivity to concurrent moves in price and volatility. In pricing models like Black-Scholes, Vanna is derived from the relationships that produce Delta and Vega, and it helps connect price dynamics to hedging decisions. Traders and risk managers monitor Vanna when assessing how a delta hedge may need adjustment if volatility expectations shift, or when evaluating the potential impact of simultaneous changes in S and σ on a position. Because Vanna combines two core risk dimensions, it is often considered in dynamic hedging frameworks that aim to keep exposure stable across varying market conditions.
If the underlying price moves while implied volatility changes, Vanna helps describe how the option’s Delta is expected to shift in response to those dual changes.
Delta · Vega · Gamma · Vomma (Volga) · Charm · DvegaDspot