# Up Gamma, Down Gamma

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Can someone please shed some light on Up Gamma and Down Gamma, I read the dynamic hedging book and I don't understand up gamma and down gamma, especially in the book the risk reversal is defined as a position that has an up gamma over some increment of a different sign than the down gamma. i really don't understand what it means?? It has confused me what risk reversal really is?

many thanks

#### Martinghoul

##### Senior member
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I don't remember the relevant part of the book, but I would guess that the terms are referring to the two different gamma values, calculated separately for a move up and down. I don't really see what this has to do with risk reversals, per se.

##### Active member
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I don't remember the relevant part of the book, but I would guess that the terms are referring to the two different gamma values, calculated separately for a move up and down. I don't really see what this has to do with risk reversals, per se.

I really don't understand but indeed in the book the risk reversal has such definition. I admit I actually don't quite understand risk reversal --- and in the book it says risk reversal has 'U' shape delta (plot against underlying) which means delta will go down first as underlying rises and then delta will go up as underlying further rises. Is that risk reversal? is that because in the area between strike prices (of long call and short put) delta is 0 and out of the area delta is positive?

#### Martinghoul

##### Senior member
2,690 276

I really don't understand but indeed in the book the risk reversal has such definition. I admit I actually don't quite understand risk reversal --- and in the book it says risk reversal has 'U' shape delta (plot against underlying) which means delta will go down first as underlying rises and then delta will go up as underlying further rises. Is that risk reversal? is that because in the area between strike prices (of long call and short put) delta is 0 and out of the area delta is positive?
Well, a risk reversal's delta isn't going to be 0 everywhere between the strikes (should be between 0 and 0.5). However, it will indeed look kinda like a 'U', which should make intuitive sense to you.

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Well, a risk reversal's delta isn't going to be 0 everywhere between the strikes (should be between 0 and 0.5). However, it will indeed look kinda like a 'U', which should make intuitive sense to you.

thanks mate, I think I always confuse myself with the plot - european options price plotted against underlying price at maturity, which is not gonna be the same as the options price plotting against underlying price before expiry, right? Why the delta should be between 0 and 0.5?

#### Martinghoul

##### Senior member
2,690 276
thanks mate, I think I always confuse myself with the plot - european options price plotted against underlying price at maturity, which is not gonna be the same as the options price plotting against underlying price before expiry, right? Why the delta should be between 0 and 0.5?
Well, it's not going to be the same, for sure. As to the delta, I am actually wrong (was thinking of a strangle, not a risk reversal).

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Well, it's not going to be the same, for sure. As to the delta, I am actually wrong (was thinking of a strangle, not a risk reversal).

So it could be zero between strike prices? why delta is 0 - 0.5 for strangle between strike prices? thanks mate.

Do you know Shadow gamma and GARCH gamma, it is really confusing when I look at the definitions, especially for GARCH gamma predicts both the future historical and future implied volatility, do you know what the 'present delta' and 'future delta' actually refers to? present delta means the underlying is spot and future delta means underlying is futures? thanks

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#### Martinghoul

##### Senior member
2,690 276
So it could be zero between strike prices? why delta is 0 - 0.5 for strangle between strike prices? thanks mate.

Do you know Shadow gamma and GARCH gamma, it is really confusing when I look at the definitions, especially for GARCH gamma predicts both the future historical and future implied volatility, do you know what the 'present delta' and 'future delta' actually refers to? present delta means the underlying is spot and future delta means underlying is futures? thanks
Just plot it and you'll see...

As to the various gammas, it's really very hard to tell without context what all these things mean.

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Just plot it and you'll see...

As to the various gammas, it's really very hard to tell without context what all these things mean.

thanks. Just for the GARCH gamma, in the book it says it is difference between present delta and future delta. it's just so confusing here what it means by saying future delta and 'future' historical volatility and 'future' implied volatility??? what the 'future' means??

#### Shakone

##### Senior member
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thanks. Just for the GARCH gamma, in the book it says it is difference between present delta and future delta. it's just so confusing here what it means by saying future delta and 'future' historical volatility and 'future' implied volatility??? what the 'future' means??

I think you're trying to run before you can walk. Take your time, go through each concept. You're not really explaining the context very well, and asking too many things, so it is hard to help.

What you seem to be talking about is models for a volatility that's changing in time, hence present and future.

Future historical volatility is probably confusing as a term, so if it does confuse you, switch the word historical with 'realised' for example or with 'statistical'.

We have info now about realised (historical) volatility, we also have implied volatility. That's now. As time goes by we'll have new data that has been realised and we could determine a new realised vol, and also the implied vol might change. So the question then is, what can we tell or estimate about these two things - the future realised vol, and the future implied vol - given that we're stuck in the present. Something? Nothing?

So we may for example pick a mathematical model, like GARCH, which models the vol and from this model derive something useful. We may consider that deep out of the money options tell us something about future vol.

Then again, I could be way off because I don't really have the context. In any case, this is reasonably advanced, and only a day or two ago you were struggling with greeks in the simple constant vol black scholes model. Slow down...

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##### Active member
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I think you're trying to run before you can walk.

We have info now about realised (historical) volatility, we also have implied volatility. That's now. As time goes by we'll have new data that has been realised and we could determine a new realised vol, and also the implied vol might change. So the question then is, what can we tell or estimate about these two things - the future realised vol, and the future implied vol - given that we're stuck in the present. Something? Nothing?

thanks a lot man. I need to think about this. About future realized vol, I think for future vol we can only have implied vol for the future, right? How can we have future realized vol given we are stuck at the present??? It's not realized yet, right?

(I don't really know why I am listed as a trading arcade... i never paid attention to that)

#### Shakone

##### Senior member
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thanks a lot man. I need to think about this. About future realized vol, I think for future vol we can only have implied vol for the future, right? How can we have future realized vol given we are stuck at the present??? It's not realized yet, right?

(I don't really know why I am listed as a trading arcade... i never paid attention to that)

Right, it's not realised.

Now suppose I give you a task. I say I'm going to toss a coin once per day, and then I say, I'm interested in the number of heads realised after 3 months, i.e. the future realised heads, and I want you to tell me something about the future realised heads right now. Will you just say to me, we can't do anything because it's not realised yet?

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Right, it's not realised.

Now suppose I give you a task. I say I'm going to toss a coin once per day, and then I say, I'm interested in the number of heads realised after 3 months, i.e. the future realised heads, and I want you to tell me something about the future realised heads right now. Will you just say to me, we can't do anything because it's not realised yet?

we know the present and can find out the implied one, but how can we have both future actual vol and future implied vol at the same time at present? It says GARCH gamma predicts both future actual vol and future implied vol, which differentiat from shadow gamma which does not make any statement as to the behavior of the future market's actual vol.

#### Martinghoul

##### Senior member
2,690 276
GARCH is a way to forecast vol. GARCH gamma is just a construct that calculates gamma based on the forecasted future vol. That's all.

Shakone

##### Active member
183 0
GARCH is a way to forecast vol. GARCH gamma is just a construct that calculates gamma based on the forecasted future vol. That's all.

thanks, mate, I will just think of this like what you said. When you trade, is it really very often put to use?

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