Vanna: dVega/dSpot or dDelta/dVol

By roma, 17 August, 2020

Vanna or dVega/dSpot or dDelta/dVol is a derivative of option vega with respect  to the price of the underlying asset, which is equivalent to a derivative of the delta with respect to volatility. According to the laws of mathematics, it also indicates the sensitivity of the option delta to changes in implied volatility.

The value of dVega/dSpot is very important for traders who trade options in order to profit from the volatility component without trying to predict the direction of the price of the underlying asset. The vanna depends on the option's moneyness, so for second-order derivatives the option's moneyness is key to trading. The risk profile of at-the-money options is different from out-of-the-money and in-the-money options.

Example. Consider an out-of-money put option. If the price of the underlying falls, then the option delta becomes more negative and approaches minus 50%. Consequently, the vega increases, as the option has the largest vega at-the-money. And if the vega increases on a falling market (usually implied volatility increases with a decline in the stock market), then the trader makes more money on the increase in volatility.

Conversely, if the price of the underlying asset rises, then the delta of the put option becomes less negative and goes to 0. Vega of the OTM put decreases thereby reducing losses from the fall in volatility, which tends to decrease in the rising market.