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?

4 posts • Page **1** of **1**

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?

Would you please explain or point to some reference related?

- sin.tutyou
**Posts:**2**Joined:**Fri Jul 13, 2012 2:58 pm

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.

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.

- mj
- Site Admin
**Posts:**1372**Joined:**Fri Jul 27, 2007 7:21 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

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

- zebullon
**Posts:**6**Joined:**Sat Jul 28, 2012 3:21 am

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

- mj
- Site Admin
**Posts:**1372**Joined:**Fri Jul 27, 2007 7:21 am

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