Vanna the Options Greek
Options "Greeks" are used collectively to determine how closely an options contract will track its underlying market. Vanna is one of these Greeks.
Specifically, Vanna is the rate at which the delta (Δ) of an option will change in relation to alterations 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. It's a second-order derivative and it's useful when a trader is making a delta- or vega-hedged trade.
As a bit of background, delta measures how much an option moves relative to the underlying asset price. Vega measures the impact volatility that alterations in the underlying asset have an option.
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. 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.
Using Vanna in Trading
Vanna is the rate at which the delta and vega of an options or warrants contract will change as the volatility and price of the underlying market change respectively. Traders who want to make an options or warrants trade where the delta or vega don't change regardless of what happens in the underlying market will want to use Vanna.
As a second-order derivative—it uses first-order options such as Delta and vega in its calculation—it can be complex and difficult to try to think of all the ways in which 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, and so do short put positions. Put options have negative Vanna, as do short call positions. This is because of an increase in volatility—vega measures this impact—will increase the changes of an option that's moving into the money.
- Based on the above guidelines, looking at Vanna can give you a quick way of assessing whether your options portfolio is net long/short calls/puts when you're holding multiple positions.
A Final Word on Vanna
As a second-order Greek, Vanna is typically only going to be useful to traders who are involved in complex options trades or to traders who hold a portfolio of options. Traders who are buying or selling just one or two options at a time, speculating on the rise or fall or lack of movement of an underlying asset, typically won't 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.