The last part of the solution to 2.6

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The last part of the solution to 2.6

Postby sin.tutyou » Mon Jul 16, 2012 12:34 pm

I am confused on why suddenly Black's formula comes into picture, and why S_T^2 can be write in as that.
Would you please explain or point to some reference related?
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Re: The last part of the solution to 2.6

Postby mj » Fri Jul 20, 2012 12:04 am

the Black formula always applies when you have a call option on a lognormal quantity.

A square of a log-normal is also log-normal. So all we have to do is rewrite it as its mean
times a log-normal with mean 1 in order to fit it into the Black formula.
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Re: The last part of the solution to 2.6

Postby zebullon » Mon Dec 29, 2014 7:49 am

I actually have a question on this one (love the book btw).
Usually, when computing E[g(x)], we use the density for X "f_X" and write E[G(x)] = int[ g(x)f_X dx]
Going back to this question I just wrote E[S_T^2]=int[ S_T^2 f_S dS] where f_S is the lognormal density for the asset, then moved to the log variables, etc..
However I took a peek at the solution to see if I was right (then I could just skip over the integration since it's mechanical) and I saw that the answer was quite far from my idea.

Could anyone give a quick hint at why my approach fails ?
Thanks
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Re: The last part of the solution to 2.6

Postby mj » Mon Jan 19, 2015 10:32 pm

you can do it that way. It's just a lot fiddlier.
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