Option Gamma

The gamma of an option indicates how the delta of an option will change relative to a 1 point move in the underlying asset. In other words, the Gamma shows the option delta's sensitivity to market price changes.

Gamma is important because it shows us how fast our position delta will change as the market price of the underlying asset changes.

Remember: One of the things the delta of an option tells us is effectively how many underlying contracts we are long/short. So, the Gamma is telling us how fast our "effective" underlying position will change.

In other words, Gamma shows how volatile an option is relative to movements in the underlying asset. So, by watching your gamma will let you know how large your delta (position risk) changes.

Option Gamma

The above graph shows Gamma vs Underlying price for 3 different strike prices. You can see that Gamma increases as the option moves from being in-the-money reaching its peak when the option is at-the-money. Then as the option moves out-of-the-money the Gamma then decreases.

Note: The Gamma value is the same for calls as for puts. If you are long a call or a put, the gamma will be a positive number. If you are short a call or a put, the gamma will be a negative number.

When you are "long gamma", your position will become "longer" as the price of the underlying asset increases and "shorter" as the underlying price decreases.

Conversely, if you sell options, and are therefore "short gamma", your position will become shorter as the underlying price increases and longer as the underlying decreases.

This is an important distinction to make between being long or short options - both calls and puts. That is, when you are long an option (long gamma) you want the market to move. As the underlying price increases, you become longer, which reinforces your newly long position.

If being "long gamma" means you want movements in the underlying asset, then being "short gamma" means that you do not want the price of the underlying asset to move.

A short gamma position will become shorter as the price of the underlying asset increases. As the market rallies, you are effectively selling more and more of the underlying asset as the delta becomes more negative.

Long Gamma Trading

Take a look at this video from Options Unversity. It provides an overview of the concept of Gamma Trading.


Comments (21)

Peter

April 30th, 2012 at 7:25pm

Hi Darryl,

The Position Delta = Delta x Contract Size x Number of Option Contracts.

In the post by Charlie, he mentioned that the contract size was 10mt (btw, I don't know what mt is, but let's just treat it as some standard unit) with the option delta being -0.2138 on 100 short call options. So, -0.2138 x 10 x 100 = 213.

For your put option question - in both cases, whether you're long or short the option the delta approaches 0 as the underlying price increases. Your long/short position just determines whether your delta will approach 0 from a positive number or a negative number. Also, the concept of ITM/OTM doesn't depend on your long/short position either. If a put has a strike price of 90 and the stock is expires at 100 then the put option is OTM. If you are long at the expiration date your position is worthless and you loss is the premium. If you are short the position is still worthless, however, you make a profit - being the premium received for selling the option.

Let me know if anything is unclear.

darryl

April 30th, 2012 at 4:37pm

Hi Peter,

I'm new to the greeks and wanted to pick up on the last comment. Why if delta is -0.2138, why would you buy 213 lots rather than 21?

In addition, 'I.e. for a long put if the underlying price increase from 50 to 60 the delta will go from -0.40 to -0.20 (longer)'. - i undertsand this as the option moves further otm and so delta moves closer to zero.

'For a short put the delta is reversed. So as the underlying price goes from 50 to 60 the short put delta will go from +0.40 to +0.20 (shorter)'. - If i'm short a put and the underlying price increases then doesn't my option move closer to/become more itm, so doesn't my delta increase?

Many thanks

Peter

March 26th, 2012 at 8:58pm

Hi Charlie,

If the contract size is 10mt then your position delta, which is the amount that you need to hedge is 213 contracts (shares).

The value change to your position according to the delta isn't with "every" 1 point move - just with the first. Because, as you've indicated the delta itself will change as the underlying changes, which is given by the gamma.

So after the underlying has moved 1 point you will have a new delta and gamma value.

Also, gamma is basis a 1 point move unless it is specified as 1% gamma.

Charlie

March 23rd, 2012 at 12:54am

Hello Peter, i have new software for options portfolio/prcing, and with a postion i have on the delta is -0.2138 (short a call) and the gamma -0.0158. If I am 100 lots short of the call (contract size = 10mt) then to be delta hedged i would need to buy 21 lots. As i understand correctly, the delta also means that the value of my position would decrease by $213 with every tick upwards. However in this instance the gamma of -0.0158 would mean that my delta goes shorter by -1.58 lots every % point higher NOT every tick higher (otherwsie gamma would be too big). The gamma value of the trade says -$15.8 which i think means the delta will decrease by this value for every % move upwards? Can you help. You agree confusing that delta is basis one tick move and gamma basis 1% move?

Nave

February 10th, 2012 at 12:53am

Great work Peter

Peter

November 5th, 2011 at 4:06am

Hi Rick,

Yes, that's correct. Both calls and puts have the same gamma value, which will decrease either side of ATM.

Rick

November 4th, 2011 at 8:45am

Hi I want your feedback
If a call, initially otm, and then the stock price approaching the exercise price, the gamma would increase, when the call is in the money, gamma would decrease?

If a put, initially OTM, then if a stock price decreases, gamma would increase, and when the put is in the money, gamma would decrease if the stock still going down?

Am I saying the right things

THX

Peter

June 5th, 2011 at 5:55am

Hi Peter87, it might help to take a look at the delta graphs on the option delta page. Take a look at the Put Delta vs Underlying Price graph.

This represents a long put - so just reverse the numbers for a short put.

I.e. for a long put if the underlying price increase from 50 to 60 the delta will go from -0.40 to -0.20 (longer).

For a short put the delta is reversed. So as the underlying price goes from 50 to 60 the short put delta will go from +0.40 to +0.20 (shorter).

Peter87

June 4th, 2011 at 8:06am

Thanks for your detailed and fast answer!
I got the part concerning calls and long puts but not the part with short puts: A short put has a concave (and negative) pay off profile. So, the higher the underlying value gets, the more approaches the pay off line the x-axis which implies that the slope (<=> delta) becomes bigger (= less negative = approaches 0).
That's why I don't get it that the position in a short put becomes shorter when the underlying price increases. In my opinion the position becomes LESS shorter (it becomes longer). But I guess there must be some reasoning errors in my argumentation!? :-)

Peter

June 4th, 2011 at 6:36am

The Delta depends on the option; call options have a position Delta and put options have a negative Delta. So, if you "sell" an option the call with have a negative Delta and the put a positive Delta.

Now, given that Gamma is positive for both calls and puts, if you sell an option your Gamma with therefore be negative.

When you're short an option and hence short Gamma both a short call and short put will "lose" Delta as the underlying price rises - this is also refered to as being "shorter".

For a call option, as the underlying price rises the option itself becomes more in-the-money and hence the Delta will move from 0 to 1. But if you are "short" the call the opposite happens meaning that the option Delta of your position will move from 0 to -1 (getting shorter).

For a put option, as the underlying price rises the option itself becomse more out-of-the-money and hence the Delta will move from -1 to 0 (getting longer). But if you are "short" the put the opposite happens meaing that the option Delta of your position will move from 1 to 0 (getting shorter).

Let me know if this is not clear.

Peter87

June 3rd, 2011 at 2:47pm

I'm a beginner in options but understand almost the whole article. What I just don't understand is this:
"Conversely, if you sell options, and are therefore "short gamma", your position will become shorter as the underlying price increases [...]"
Delta (as first derivative) is negative and grows with increasing Underlying price, so it becomes LESS negative which means "less short" <=> "more long" !?!?!?!?
I would appreciate your feedback!

Peter

November 3rd, 2010 at 4:54am

Are you talking about the video on this site above? That's where I say "take a look at this video". Then I provide a link to the OU site. The video above on "this" site does indeed do more than "describe" what gamma is and elaborates on gamma trading.

Please let me know if I have missed something or if you think the video above is incorrect.

trader1

November 2nd, 2010 at 11:20pm

i clicked on the "options university" link under the long gamma trading heading,
it says you can see a video that gives an overview of gamma trading.
instead of a video that gives an over view of gamma, it is a 100 percent sales video for options university. NO GAMMA EVEN MENTIONED. rip off.

sam

July 28th, 2010 at 9:06pm

you are right. delta of put is decreasing function from -1 to 0 as the stock price increases. I was thinking in terms of absolute value of delta...

Peter

July 28th, 2010 at 6:10pm

Hi Sam, it's a good question. You have to remember that a put's delta is negative so with a positive gamma and an increasing stock price the delta of a put becomes less negative - or "longer". The more the stock rallies the closer the put's delta approaches zero as more gamma is added to it.

Call options, with a positive delta and positive gamma will also "get longer" as the stock price rises. The higher the stock moves away from the strike price the closer the call option's delta approaches 1.

sam

July 28th, 2010 at 4:14pm

May be I am missing something. Mathematically, gamma is always positive for both call and put.

But as the stock price increases, shouldn't the put have negative gamma as the graph of put delta vs stock price is decreasing? Please someone clarify

Seth Baker

February 9th, 2010 at 3:04pm

This is interesting stuff. I use google to help me find stuff about options. One cool site has a different approach - they claim to not have an opinion on the market. Rather, they work with you on which type of trade to make, based on the Greeks, etc. I may spell this wrong, but I think it's http://www.timeforoptions.com

Peter

October 8th, 2009 at 7:05pm

Hi Anthony, I agree that the video doesn't get off to a good start...I link directly to the video on the OU site. They've changed the video to what they've had previously, which provided a longer introduction.

At the start of the video Ron has already begun discussing "short gamma", where if you are short gamma and the market is going down your position gets "longer" i.e. your delta position grows. That's what he means when he says "buying deltas" on the way down.

Do you think my description (not the video) above differs from what you've read elsewhere? If so, let me know where the contradiction is and if I'm wrong I'll correct the content accordingly.

Thanks for the feedback!

Anthony

October 7th, 2009 at 10:39pm

I am learning to trade options by the greeks (delta, gamma, theta, vega) but have traded options for many years. I have looked up several definitions and am doing an online course. This definition here and the subsequent video are by far the most confusing I have ever come across. The video begins with "In a sense on the way down, our short gamma position is buying deltas for us...". How in the heck can someone trying to understand Gamma as a definition begin to understand this.

Peter

September 20th, 2009 at 8:09pm

Thanks for the suggestion...much appreciated. I'll write up something on delta neutral trading and a bit more on gamma scalping.

Howdy

September 20th, 2009 at 10:38am

I have basic knowledge of options buying and selling calls and puts.
I would appreciate it if more detailed explanation is added in for gamma and delta trading. I am still confused as to how gamma trading works.

Thanks

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