# volatility and gamma

##### Active member
183 0
Hi, can I ask why when volatility is low, the gamma of at-the-money options is high while the gamma for deeply into or out-of-the-money options approaches 0? and why When volatility is high, gamma tends to be stable across all strike prices?

many thanks

#### Shakone

##### Senior member
2,458 665

Not every option has similar behaviour with respect to the greeks. Are you talking about typical vanilla calls?

Last edited:

#### Martinghoul

##### Senior member
2,690 276
Indeed, like Shakone says, why not a single thread?

In answer to your question, what is the formula for calculating option gamma (using B-S)?

##### Active member
183 0
Indeed, like Shakone says, why not a single thread?

In answer to your question, what is the formula for calculating option gamma (using B-S)?

Thanks Martinghoul and Shakone. when I submitted the 1st question I hadn't thought about the 2nd questions, yeah it'd be more clear if all questions appeared in one thread.

yes, B - S formulas, that's why it is a bit confusing. thanks mate

##### Active member
183 0

Not every option has similar behaviour with respect to the greeks. Are you talking about typical vanilla calls?

Yes mate, typical vanilla options but not restricted to calls. thanks mate

#### Shakone

##### Senior member
2,458 665
Ok, so Delta represents the change in the derivative price with respect to the underlying.

Now consider a call option with a strike of 100, and suppose price is at 1, we're way out of the money. That option is unlikely to be worth much (this depends on vol and time to maturity - but set these aside for a second), because it's very unlikely that price will rise above 100. If price is at 5, it's still unlikely to be worth much for the same reason. So a move in the underlying from 1 to 5 won't change the price of the call option a lot. Because of that, the delta is low and also won't change much.

Because the delta won't change much on a move from 1 to 5, that means the gamma is low. With me so far?

##### Active member
183 0
Ok, so Delta represents the change in the derivative price with respect to the underlying.

Now consider a call option with a strike of 100, and suppose price is at 1, we're way out of the money. That option is unlikely to be worth much (this depends on vol and time to maturity - but set these aside for a second), because it's very unlikely that price will rise above 100. If price is at 5, it's still unlikely to be worth much for the same reason. So a move in the underlying from 1 to 5 won't change the price of the call option a lot. Because of that, the delta is low and also won't change much.

Because the delta won't change much on a move from 1 to 5, that means the gamma is low. With me so far?
thanks a lot mate, that makes sense.

#### Shakone

##### Senior member
2,458 665
Ok, the same logic applies to when you are vastly in the money. If the price of the underlying was 2000, then this option is very likely to end up in the money, and so you'll need to be holding the underlying for each option, which means delta is at 1 (or close to 1), and a change from 2000 to 1990 or whatever isn't going to change the delta much = gamma low again.

When you are at the money or thereabouts, you don't know whether it will finish in the money and be exercised or not, and even a small change in the underlying can make a big difference.

##### Active member
183 0
Ok, the same logic applies to when you are vastly in the money. If the price of the underlying was 2000, then this option is very likely to end up in the money, and so you'll need to be holding the underlying for each option, which means delta is at 1 (or close to 1), and a change from 2000 to 1990 or whatever isn't going to change the delta much = gamma low again.

When you are at the money or thereabouts, you don't know whether it will finish in the money and be exercised or not, and even a small change in the underlying can make a big difference.

I see, thank you very much!

Replies
1
Views
675
Replies
1
Views
261
Replies
4
Views
760
Replies
12
Views
33K
Replies
8
Views
1K