down and out call in a skewed environment

mensatrader

Active member
183 0
Hi all, is it true that a knock out call will be cheaper in a positive skew than in a flat skew? why?

From my understanding, The knock out call (down and out call) can be replicated by long one vanilla call with the same strike K1 and short a symetrical put K2 with ratio of square root of k1/k2 puts for one call, the barrier is the geometric average of k1 and k2. If in a positive skew, then the put should be cheaper than the call, right? Hence, overall the risk reversal costs more than in a flat skew, so why the regular knock out call are cheaper than in a flat skew?

many thanks
 

Shakone

Senior member
2,458 665
Because the buyer of a down-and-out call is short skew, i.e. skew goes up, price goes down.


Maybe :)
 
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mensatrader

Active member
183 0
Because the buyer of a down-and-out call is short skew, i.e. skew goes up, price goes down.


Maybe :)

thanks mate. are you sure down and out call is not long skew? when market goes up aggressively, the vega/gamma goes up as well; when market goes down and close to barrier, the vega should decrease, so it looks like long skew, right?
 

Shakone

Senior member
2,458 665
thanks mate. are you sure down and out call is not long skew? when market goes up aggressively, the vega/gamma goes up as well; when market goes down and close to barrier, the vega should decrease, so it looks like long skew, right?

For calls:

Long a down and in would be long skew. Long a down and out, short.

It may help to think that for a down and out you start with an option but it knocks you out if it hits the barrier, and you'll have nothing. If the underlying asset is more volatile, all else being equal, aren't you more likely to be knocked out (which you don't want). Lower volatility, you'll be less likely to be knocked out.

By contrast with a knock in you have nothing to start with, and will have nothing unless the barrier hits, so you want the barrier to be hit, you want the underlying to be more volatile.

Hope that helps some.
 
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mensatrader

Active member
183 0
For calls:

Long a down and in would be long skew. Long a down and out, short.

It may help to think that for a down and out you start with an option but it knocks you out if it hits the barrier, and you'll have nothing. If the underlying asset is more volatile, all else being equal, aren't you more likely to be knocked out (which you don't want). Lower volatility, you'll be less likely to be knocked out.

By contrast with a knock in you have nothing to start with, and will have nothing unless the barrier hits, so you want the barrier to be hit, you want the underlying to be more volatile.

Hope that helps some.

what you said is vega is concave for all types of regular k-out option, and vega is convex for all regular k-in options, but I guess this is not entirely about long/short skew (or third moment). For down and out call, in a positive skew (which means higher strikes has higher IV), the vega is still increasing when market rallies aggressively even though it is concave to volatility (which means it is increasing at a decelerated rate), it is still increasing. I think for a k-out option, when the barrier/trigger is above the strike (which refers to an up and out option), it is short skew.

Anyway, those thoughts were from the book, I still don't quite understand the long/short skew.
 
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Shakone

Senior member
2,458 665
what you said is vega is concave for all types of regular k-out option, and vega is convex for all regular k-in options, but I guess this is not entirely about long/short skew (or third moment). For down and out call, in a positive skew (which means higher strikes has higher IV), the vega is still increasing when market rallies aggressively even though it is concave to volatility (which means it is increasing at a decelerated rate), it is still increasing. I think for a k-out option, when the barrier/trigger is above the strike (which refers to an up and out option), it is short skew.

Anyway, those thoughts were from the book, I still don't quite understand the long/short skew.

So you agree that a long down and out call is short skew then? Not sure if there was another question, but yes these things are messy to think about.
 
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mensatrader

Active member
183 0
So you agree that a long down and out call is short skew then? Not sure if there was another question, but yes these things are messy to think about.

down and out call is not short skew, as long as vega/gamma increase when markets experience strong rally, it is a long skew..
 
 
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