In one of our previous blogs, we have seen options Greeks wiz delta, gamma, theta, Vega, and rho. If these are the options Greeks then what is Vanna? Vanna also is an Option Greek but it is a second-order option Greek. This means it is the second derivative of the value of an options contract used to understand the different dimensions of risk involved in trading options. It measures the impact of changes in price and changes in the volatility of the underlying market. This blog is a dedicated blog on Vanna in options.

In this blog, we have covered Vanna options Greek definition, or what is Vanna? Vanna options Meaning, How Vanna Works? Importance of Vanna in options trading, Vanna options Formula, how to manage Vanna in the portfolio. To understand Vanna in option, it is important to know about the 1st order options Greek. If you are still unfamiliar with these Greeks, take some time to review them. You can read our __Options Greek__ blog to know about first-order option Greeks. When the delta or Vega do not change with respect to the happenings in the underlying market then the options traders make use of Vanna in such a situation.

**What Is Vanna Options Greek?**

The second-order derivative of option Greek which measures the movements of the delta with respect to changes in implied volatility is called the Vanna Option Greek. Changes in first-order Greeks (Delta, Rho, Vega, Theta) due to underlying conditions such as price fluctuations or interest rate changes are measured by second-order Greeks. As Vanna is related to options and is represented by a Greek letter it is called an option Greek. Options Greeks are used with one another to identify how closely an options contract will track its underlying market. They represent the price sensitivity of derivatives to changes in the underlying assets or the parameters by which those assets are measured.

Vanna in options is also called an options volatility Greek. It can also be defined as the rate of change of Vega with respect to changes in the underlying price. It measures the rate at which the delta of an option will change concerning alterations in the volatility of its underlying market and the rate at which the Vega of an options contract will change with respect to the changes in the price of its underlying market. The relationship between the two first-order Greeks i.e. delta and Vega is assessed by the Vanna. Measuring a Vanna is useful while making a delta-hedged or Vega-hedged trade. The value of Vanna for the CALL option is positive whereas the PUT options have negative Vanna. This is because an increase in volatility will increase the probability of an option moving into the money.

**How Does Vanna Work?**

Till now you must have got the basic idea about the Vanna option Greek. Let's see how Vanna works. One thing that is important to note here is that Vanna is not equal over the surface of the options. For better understanding see the graph below.

Assume that it is a long call of strike price =100; 30 days; vol=20%

From the graph, you can see that the options with the high Vanna are the wings that are fairly Out-of-The-Money (OTM). Vanna is equal to zero when the price of an underlying reaches the strike price or we can say that when it is At-The-Money (ATM). This is exactly opposite to the gamma which always is the highest for At-The-Money. This shows that changes (Increase or decrease) in volatility do not affect the options. As the price increases far enough away from the spot price, Vanna decreases.

Remember that the option cannot have a delta over 1 (Δ>1). Therefore, any increment in the delta of one option corresponds to a decrement in the delta of the other option.

Now let's see another graph showing the comparison of Gamma, Vanna, and the Volga for their values with respect to option price.

Traders who make use of Vanna should remember the following thing,

Call options have positive Vanna, and hence short put positions.

Put options have a negative Vanna, and therefore short call positions.

This is because an increase in volatility will increase the chances of an option moving In-The-Money (ITM). As a result, when you are holding multiple positions, just by looking at Vanna you can quickly get an idea about whether your options portfolio is net long/ short/ calls/ puts.

**Importance of Vanna in options trading**

Vanna is crucial for a market maker who manages an inventory across multiple strikes, expirations, and tickers. It is used to understand the all-dimensional risk involved in options trading. Vanna represents the joint relationship of changes in both volatility and the underlying asset price. It is generally used by the traders who are involved in complex options trades or the traders who hold a portfolio of options to understand the risk. Traders won't need to consider a Vanna calculation if they are buying or selling just one or two options at a time and speculating on the rise, fall, or lack of movement of an underlying asset.

**Vanna options Formula**

In the Black Scholes model, Vanna gets calculated using the following formula:

*Where,*

S = Stock Price

r = Risk free rate

o = Implied volatility

t = Current period

T = Expiry Date

q =Dividend rate

Assuming dividend (q) = 0 the above equation simplifies to,

**How To Manage Vanna in Portfolio**

To avoid Vanna, never sell option wings naked. It doesn’t mean that you should never sell wings, you can sell the wings but be aware of the risk. If the risk is too large, size down if needed, or move to a risk-defined structure. One can buy the OTM wings and have Vanna work for them without shorting Vanna. If you stress your position, you can see what effect Vanna will have and allow you to see if you are comfortable with it. On the other hand, if the position moves against you, take the loss and move on before your risk becomes too high.

**Conclusion**

Vanna is a second-order Greek and at the start, it may seem difficult. But Vanna is nothing but the change in an options delta for any change in implied volatility. The average retail investor who places small or risk-defined trades should not be concerned with Vanna. Investors who are selling Out of The Money options with large risk should consider the effects of Vanna and should size down or choose risk-defined structures that mitigate Vanna risk.

Call options have positive Vanna, and hence short put positions.

Put options have a negative Vanna, and therefore short call positions.

=> this is totally wrong! according to the first picture in this post, otm call itm put have positive Vanna, otm put itm call have negative Vanna. OTM Call have positive Vanna to have its Vega getting larger when underlying rise toward the strike, and have its Vega getting smaller when underlying rise away the strike. Please correct me if I am wrong. Thanks!