Just when you thought you had it figured out with the firstorder greeks, you find out there are second order greeks as well.
The first order greeks are the sensitivities of different factors to the price of an option.
Yet that is not all.
The secondorder greeks are sensitivities affecting the firstorder greeks, therefore indirectly affecting the price of an option.
This article will explore all of the secondorder greeks and talk about some of their sensitivities.
We will also discuss the importance of secondorder greeks in options trading.
This article will be a basic overview.
If you are curious about going deeper into one of these greeks or reviewing the first order greeks feel free to explore the links in this article.
Contents




 Why Are Second Order Greeks Important in Options?
 Gamma
 Vanna
 Vomma
 Charm
 Veta & Vera
 What About the Third Order Greeks?
 Do I Need To Monitor These Second Order Greeks To Trade?
 Concluding Remarks



Why Are Second Order Greeks Important in Options?
Secondorder greeks are a fundamental part of options themselves.
In fact, without secondorder greeks, an option can simply not exist.
For example, without second order greeks, one could sell a delta 30 call, which would be equivalent to shorting 30 shares.
While these are somewhat similar on inception, the payoffs at expiration are very different, as shown below.
The black line shows our short call, and the yellow line shows the short shares.
So underestimating the importance of secondorder greeks is never a good idea.
Nevertheless, as they affect the first order greeks, their importance is naturally less than the first order greeks.
Some options gurus will attempt to sell services or just appear smart by rattling off the secondorder greeks constantly, with almost no regard to the basic firstorder greeks.
This is like buying all the best golf equipment without ever taking a golf lesson.
Sure, you may look good in the parking lot, but that doesn’t mean much.
If you are reading this and are new to the first order greeks, here are some refreshers first.
Review of Delta
Review of Vega
and finally – Theta
Now, let us introduce our secondorder Greeks!
Gamma
Gamma measures the rate of change of an options delta for a given change in an options price.
Remember our graph above of the short delta 30 call?
It looks so much different from the short shares because as the price of the underlying changes, the option’s delta changes as well.
This is gamma in effect.
If there is onesecond order Greek to learn inside and out, it is gamma.
This is as it has very large effects on the moves in the price of an option.
So much so that many learn about it along with the firstlevel greeks.
Gamma also has a very strong relationship to theta.
As the buyer of an option, we are buying gamma and selling theta.
As an options seller, we are selling gamma and buying theta.
As we can see, atthemoney options with very little time to expiry have the most gamma.
These also have the most theta.
For all traders, especially those trading shorterdated options, understanding gamma is a must.
Vanna
Vanna measures the change in delta for any given increase or decrease in the level of implied volatility.
The options that have the most Vanna are outofthemoney options.
This is because a delta 50 option will not change if the level of implied volatility increases.
In contrast, a delta 10 option will gain a significant amount of delta if the level of implied volatility goes drastically higher.
We can see this Vanna exposure from the chart below.
Therefore for atthemoney options and small positions, Vanna is not too important.
If you are trading naked outofthemoney options, especially with large positions, make sure you know Vanna risk.
Vomma
Vomma measures the rate of change in an options vega for a change in implied volatility.
We can see from below the chart that Vega, Vomma is highest for outofthemoney options.
Charm
Charm measures the rate of change in an options delta for a given passage of time or theta.
It is also commonly referred to as the delta decay of an option.
Charm is also very similar to Vomma and Vanna in that it affects outofthemoney options the most.
It also affects shorterdated options the most, as these decay the fastest.
Charm can be very important for delta hedgers or people who want to maintain constant exposure for outofthemoney options.
Even if the price does not move, these options will lose their delta.
This can result in being over hedged if you are short or unable to take full advantage when a move comes if you are long.
Veta & Vera
Veta measures the change of vega with time (theta).
Vera measures the change in the rate of rho with respect to volatility.
Veta and Vera are two of the secondlevel greeks that are not commonly used.
Even the first order greek of Rho has been of little importance due to how lowinterest rates are.
That being said, if interest rates were to move dramatically, longerdated options would be affected.
What About the Third Order Greeks?
Just as there are secondorder Greeks, there are also thirdorder greeks.
For the average retail trader, these will have little direct significance.
Focusing on these will most likely confuse someone further and distract them from the more important greeks.
Though for building models and higherlevel finance, they are relevant.
Do I Need To Monitor These Second Order Greeks To Trade?
For most beginner traders, except for gamma, it is not necessarily to be too concerned with calculating your secondorder greeks.
These secondorder greeks can often have negligible effects for riskdefined positions such as iron condors and tight verticals.
Hence sometimes, a strong understanding, while helpful, may not be necessary.
Despite this, it is critical to understand at the least that the firstlevel greeks are not constant and will change over time.
This may result in some very different greek exposures as a trade progresses.
By monitoring your firstorder greeks as a trade progresses, you can adjust for the effects of secondorder greeks as the trade progresses.
This can help reduce variance and limit the risk on a position.
Concluding Remarks
The secondorder greeks are a very important component of options themselves.
While they are naturally less important than the firstdegree greeks they are derived from, they still explain why options exposures change over time.
Depending on the position’s structure, time to expiry, and delta, a position may have a minimal or relative significant exposure to these seconddegree greeks.
Understanding a little about them and how they affect our main greeks can help us manage the hidden risks that a trade might have.
Trade safe!
Disclaimer: The information above is for educational purposes only and should not be treated as investment advice. The strategy presented would not be suitable for investors who are not familiar with exchange traded options. Any readers interested in this strategy should do their own research and seek advice from a licensed financial adviser.
The post Blog first appeared on Options Trading IQ.
Original source: https://optionstradingiq.com/secondordergreeks/