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Topic Title: Question regarding Digital Option and skew
Created On Fri Nov 28, 08 06:24 PM

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AutumnTale
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Fri Nov 28, 08 06:24 PM

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I have a question:

I am tring to price a digital option, and I use Vanna-Volga method for interpolation.
And I use the two call option to replicate that digital option.
The question is: Should I use one volatility for two different volatility to replication this digital option?
The reason I am asking this question is: these two approach gives different results, and the difference is equal to Vega*slope of skew surface.

Thanks a lot for your help.

PaperCut
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Fri Nov 28, 08 07:29 PM

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Two different ones. That's how the method is able to capture the skew sensitivity of the structure.

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HOOK
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Fri Nov 28, 08 07:49 PM

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Indeed, two different ones.

The reason why the difference is vega times the slope of the surface, is that a binary option can be seen as the derivative of a call with respect to the price.

If your vol also changes with the strike, then the correct price will be :

Binary : N(d2) + (dcall/dvol)*(dvol/dK)

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amit7ul
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Tue Dec 02, 08 11:33 AM

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derivative of a call wrt strike

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HOOK
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Tue Dec 02, 08 02:12 PM

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Quote
Originally posted by: amit7ul
derivative of a call wrt strike

Absolutelly, my mistake !

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