Vanna, Explanation of the Options Greek

What vanna is, and how to use it

trader assessing vanna options data
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Vanna is one of the options greeks which are collectively used to determine how closely an options contract will track its underlying market. Specifically, vanna is the rate at which the delta (Δ) of an option 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 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.

As a brief recap, delta measures how much an option moves relative to the underlying asset price. Vega measures the impact volatility changes in the underlying asset have on an option. 

Vanna Calculation

Vanna is the second derivative of the value of an options or warrants contract, with respect to the price and the volatility of the underlying market. The vanna calculation can been seen in this image.

Vanna's primary function is to assess the relationship between the first order greeks of delta and vega. In other words, it looks at the joint relationship of changes in both volatility and the underlying asset price.  

Vanna Uses 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.

Because vanna is a second order derivative (uses first order options such as delta and vega in its calculation), it can be complex thinking of all the ways that delta and vega can affect vanna (or how vanna will affect delta and/or vega).

Here are a few points to consider:

  • Call options have positive vanna, so do short put positions. Put options have negative vanna, as do short call positions. This is because an increase in volatility (vega measures this impact) will increase the changes of an option moving into the money
  • When holding multiple positions, looking at vanna can give you a quick way of assessing whether your option portfolio is net long/short calls/puts, based on the above guidelines. 

Final Word on Vanna

As a second order greek, vanna is typically only going to be used by traders involved in complex options trades, or traders holding a portfolio of options. Traders who are buying/selling one or two options at a time, speculating on the rise or fall (or lack of movement) of an underlying asset, typically won't ever need to consider a vanna calculation. The primary function of vanna is to look at the joint relationship of changes in both volatility and the underlying asset price on an option(s). 

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