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equivalent Black-Scholes volatility

Joined
8/11/11
Messages
124
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278
Hi all,

I wonder if the following makes sense and if so, if anyone can recomend me any paper or similar

To price exotic equity options, we are using models that consider the vol smile (local vol and stochastic vol). I wonder if we could compute a BS vol equivalent.

in other words, once we got the price of the option (which in general doesn't have a closed formulae), is there any way to compute a flat vol (i.e. BS vol)?

We think of using this flat vol to have the feeling if the behaviour of our calculator is right (BS vol goes up, price goes up, etc.)

I searched on the forum but didn't find anything...

Thanks!!!
 
Couldn't you just use the price calculated from whichever model you are using and then invert the Black Scholes formula (using the newton raphson method) to get the BS equivalent?

Maybe I'm not understanding you correctly.
 
yeap, that's what we though for options with closed form

But in general, we use montecarlo and there is we find problems... for me doesn't make sense to apply a solver in a montecarlo method... or maybe yes?

what other ways are there?
 
yeap, that's what we though for options with closed form

But in general, we use montecarlo and there is we find problems... for me doesn't make sense to apply a solver in a montecarlo method... or maybe yes?

what other ways are there?

don't think there's any other way really.. but most exotic options should have closed form solutions in a black-scholes framework right.. in any case even if there wasnt i think you're basically stuck with a root finding algorithm.. just putting this out there also: i think the results you get will be unintuitive and pretty meaningless
 
that's my other question! doesn't it make sense this BS vol?

I plan to use it to see if the movement in the option's price makes sense or not (among other things, like to movement is the spot)


i'm not really sure what you're talking about to be honest.. the vol for vanilla strike you get on an implied volatility smile contains a good amount of intuitive information about the market's perceived conditional expectations of volatility given certain spot movements.. the vol you'd get when setting the smile price of an exotic equal to a B-S equation output will contain weird distortions depending on what kind of exotic you are using and will likely cause the number to not make sense.. the reason being the one unknown input into a vanilla price is the implied vol, whereas an exotic takes the entire vol smile and/or surface, which renders your analysis of a singular implied vol to value an exotic meaningless.. what kind of exotic were you thinking of doing this with by the way?
 
i'm not really sure what you're talking about to be honest.. the vol for vanilla strike you get on an implied volatility smile contains a good amount of intuitive information about the market's perceived conditional expectations of volatility given certain spot movements.. the vol you'd get when setting the smile price of an exotic equal to a B-S equation output will contain weird distortions depending on what kind of exotic you are using and will likely cause the number to not make sense.. the reason being the one unknown input into a vanilla price is the implied vol, whereas an exotic takes the entire vol smile and/or surface, which renders your analysis of a singular implied vol to value an exotic meaningless.. what kind of exotic were you thinking of doing this with by the way?

That's what I was thinking. Wouldn't obtaining the Black Scholes volatility equivalent only make sense when you're using a model other than Black Scholes (such as Heston) to obtain the price of a European vanilla option and then using that price in BS to solve for the volatiltiy?

It doesn't make sense for exotic options.
 
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