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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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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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