# What Is Vanna?

DEFINITION

Vanna is one of the second-order Greeks used to understand the different dimensions of risk involved in trading options. It is the second derivative of the value of an options or warrants contract and measures the impact of changes in price and changes in volatility of the underlying market.

## What Is Vanna?

Vanna measures the rate at which the delta (Δ) of an option will change (in relation to alterations in the volatility of its underlying market) and 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 used to assess changes in the relationship between the Greeks delta (Δ) and vega (v) in trading options.

Options Greeks are used collectively to determine how closely an options contract will track its underlying market. They represent how sensitive the prices of derivatives are to changes in the underlying assets or the parameters by which those assets are measured.

They are called "Greeks" because they are usually represented with Greek letters.

Vanna is a second-order Greek, which means that it is a second-order partial derivative of options prices with respect to different variables. Second-order Greeks measure how quickly first-order Greeks (delta, rho, vega, theta) change due to underlying conditions such as price fluctuations or interest rate changes.

The delta (Δ) of an option measures the rate of change between the option's price and the price of the underlying asset. The vega (v) of an options contract represents the rate of change between an option's value and the volatility of the underlying asset.

Vanna is useful to measure and consider when a trader is making a delta- or vega-hedged trade.

## How Does Vanna Work?

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. In other words, it looks at the joint relationship of changes in both volatility and the underlying asset price.

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.

Delta is a measure of change. It measures how much an option moves relative to the underlying asset price. Vega is a measure of sensitivity. It is the derivative of the option value in relation to the volatility of the underlying asset.

As a second-order derivative—meaning that it uses the first-order options 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.

Traders using vanna will want to consider a few different points.

• Call options have positive vanna, and so do short put positions.
• Put options have negative vanna, as do short call positions.

An increase in volatility—measured by vega—will increase the changes of an option that's moving into the money. As a result, looking at vanna can give you a quick way to assess whether your options portfolio is net long/short calls/puts when you're holding multiple positions.

## Do I Need to Know Vanna?

As a second-order Greek, vanna is typically most 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, and who are speculating on the rise, 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. If that isn't relevant to your trade—or if your trade is not complex enough to consider these factors—you do not need to work with a vanna calculation.

### Key Takeaways

• Vanna is one of the second-order Greeks that are used to understand the different dimensions of risk involved in trading options. It looks at the joint relationship of changes in both volatility and the underlying asset price.
• 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.
• Call options have positive vanna, and so do short put positions. Put options have negative vanna, as do short call positions.
• As a second-order Greek, vanna is typically most useful to traders who are involved in complex options trades or to traders who hold a portfolio of options.