# Options Trading 101: Part 6 - The Option Greeks

Updated: Feb 25, 2019

**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.**

Deltameasures 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.**

Thetameasures 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.**

Vegameasures 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 it’s overall impact.**

GammameasuresDelta’ssensitivity 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 long-term trades have lower***Gamma*. This is one of the main reasons why short-term option trading comes with higher risk.__Read more about contract length by clicking here.__**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 too 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. Remember the VIX Index is also a derivative of the S&P 500 derivatives market. The layering is enough to drive most people crazy so the vast majority of traders don’t even pay attention to them. However a few of them are useful and worth an explanation.**

Charmmeasures the rate of change ofDeltaover 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.**

Colormeasures the rate of change ofGammaover 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.**

DvegaDtimemeasures the rate of change ofVegawith 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.**

Speedmeasures the rate of change in Gammawith 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 likey won’t be for yours either. Anyway 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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