Options Trading 101: Part 6  The Option Greeks
Feb 09, 2017
This article was originally posted in January 2013 on my other website which is why the example is from so many years ago, but everything still applies today, so fellow math geeks enjoy!
Understanding “the Greeks” allows option traders to objectively calculate expected changes in the value of their positions given various changes in volatility, stock price, and time decay.
There are four very important derivative quantities for option trading, each represented by a greek symbol. These are the most talked about, the easiest to understand, and in most cases the most useful of all the option Greeks.
Below is an actual example of a live Iron Condor that I traded. The yellow highlighted lines are the 4 strikes of the Iron Condor and as you can see this trade is for a January 2013 expiry. I will use this example to explain the four main greek symbols and show you why it is important for an option trader to understand them.
Delta measures an options’ sensitivity to changes in the underlying assets’ price

In the picture above you can see that the Delta of the trade is 148.58$. What that means is if all other variables are held constant and we only look at a change in price, if the price of the SPY goes up by 1$ tomorrow my Iron Condor will lose 148.58$ in value. If the SPY goes down by 1$ my Iron Condor will gain 148.58$ in value.

Delta is especially important for Iron Condor traders because we always try to stay as market neutral as we can. Through proper allocation, hedging, and layering, it is my goal to keep my Delta as low as possible to insulate myself against the effects of large price changes in the underlying being traded.
Theta measures an options’ sensitivity to time decay.

For the Iron Condor above you can see that the Theta value is 24.25$. This means that if all other variables are held constant, the passage of one day will increase the value of the position by 24.25$.

Theta is one of the most important greek symbols to understand. Nearly all of our option trading is focused on market neutral trades that profit through the passage of time. So it is extremely important to manage our trades to attempt to always stay Theta positive. That would mean our positions will gain value with each passing day. The passage of time is the only guarantee in trading. Being Theta positive means time is always on our side.
Vega measures an options’ sensitivity to changes in the underlying asset’s volatility.

The Vega of that Iron Condor is 188.62$. This means that for every 1% the volatility of the SPY increases my option position will decrease in value by 188.62$. For every 1% the volatility decreases my position will increase in value by 188.62$.

Vega is another very useful option greek because when we sell an Iron Condor we are selling volatility. It’s very important to be able to predict what effect volatility changes will have on our position. Since we can’t control Vega directly through the Iron Condor, sometimes hedging is required to reduce its overall impact.
Gamma measures Delta’s sensitivity to changes in the underlying assets’ price.

Gamma can be a little difficult to understand because it’s a second order derivative measuring price change effects on the first order derivative Delta. Instead of using numbers it’s best to just conceptualize it. Iron Condors always have negative and increasing Gamma which means that the Delta of my trade is going to be increasing as time goes by. What that does is make my trade increasingly susceptible to price movements as it gets closer to expiry.

Short term trades have higher Gamma and longterm trades have lower Gamma. This is one of the main reasons why shortterm option trading comes with higher risk.

Since Gamma is always increasing with the passage of time it becomes increasingly important to monitor as we approach the options expiration date. Gamma shows us that options near the end of their cycle are extremely sensitive to price changes which is why all our option trades are closed out well before their expiration date.
So those are the four main Greeks that most option traders pay attention to. For the VTS Iron Condor strategy, through proper trade selection and hedging when necessary we try to remain Delta neutral and Theta positive, all the while remaining insulated from the potentially negative effects of high Gamma and Vega.
Now I intentionally said the four “main” Option Greeks people pay attention to because in actuality there are another ten more besides those that very few people talk about or even know about. In most cases these can be more complex because sometimes they are second and even third order Greeks which means they are in some cases a derivative of a derivative of a derivative. Then factor in that some of the instruments we trade options on are also derivatives. The VIX Index is a derivative of the S&P 500 derivatives market, the volatility ETPs like XIV are a derivative of the VIX futures market. The layering is enough to drive most people crazy so we do try to keep things as simple as possible. Most of the higher order Greeks we don't have to pay attention to, but a few of them are useful to at least conceptualize (you never have to calculate anything) and worth an explanation.
Charm measures the rate of change of Delta over time.

Charm is represented mathematically as Delta over a year so it can be useful in determining the expected changes in Delta over a given number of days.

If you’re trying to Delta hedge an Iron Condor with puts or calls of different expiration or trying to Delta hedge over a weekend for example, Charm can be quite useful in predicting what your position will look like over the next few days.
Color measures the rate of change of Gamma over time.

Remember Gamma is already a second order derivative of Delta, so Color is now a third order twice to the underlying asset and once to time.

It can get a little complicated. For Iron Condor traders it’s not actually that important because we usually Delta hedge and monitor Gamma as is, but it can be quite useful for traders who want to Gamma hedge a broader portfolio.
DvegaDtime measures the rate of change of Vega with respect to time.

Basically the same as the above two. If a trader wanted to know more specifically what Vega changes to expect over a weekend or a few trading days, dividing by 100 and backing out the number of days per year we can arrive at a reasonably accurate value.

The only practical use for me is measuring the effectiveness of any hedges I may have on at the time.
Speed measures the rate of change in Gamma with respect to changes in price.

For the majority of option traders out there, Speed is rarely a consideration. For me however, and more specifically for my option trading done directly on the VIX Index I quite often need to consider the affects of both changes in Delta and changes in Gamma simultaneously when adding new positions so speed can be useful. It’s not enough to know what they will look like one or two points away because the VIX can move so quickly. I need to put actual numbers to the trades and understand the “acceleration” of Delta and Gamma as prices move around.
The rest of the higher order greeks aren’t that important for my trading and very likely won’t be for yours either. Just to be thorough I will list the rest of the option derivatives and all their funny names:

Vanna or DdeltaDvol measures sensitivity of Delta with changes in volatility

Vomma measures rate of change to Vega with changes in volatility

Rho measures sensitivity to interest rates

Lambda measures percent changes in value per change in price, also called elasticity

Ultima is the third order derivative of Vomma with respect to changes in volatility

Zomma is the third order derivative of Gamma with respect to changes in volatility

Vera measures the rate of change of Rho with respect to volatility
For those of you who actually made it to the end of this article without falling asleep, those are the Option Greeks. We have the four main ones that we pay attention to on each and every trade we make (delta, theta, vega, gamma). Then there are three or four other high order Greeks that may also be important depending on what kind of trade I’m making and what style of hedging I’m planning on implementing (charm, color, DvegaDtime, speed). These are the ones that if you were to ask the average option trader what they are and how they are used, it’s likely most of them wouldn’t know. They are very rarely talked about due to their complexity and they won’t show up on peoples trading platforms so it requires some good old fashion math to understand and use them in a practical sense for trading. After those, there’s about seven more Greeks listed that you can basically just ignore.
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