Re: Expected Value of Positive Part of Lognormal Random Var

beliavsky_at_aol.com
Date: 02/28/05 

Date: 27 Feb 2005 17:58:26 -0800

Bob Buchanan wrote:
> Hello,
>
> I am trying to find a detailed derivation or create a detailed
> derivation for the expected value of the following quantity:
>
> Suppose X is a lognormally distributed random variable with
parameters
> mu and sigma. Suppose K > 0 is a constant. I want to derive the
> expression for the expected value of (X-K)^+, which is the "positive
> part" of the expression X-K.
>
> To give you more background on my request, I have found the final
> answer in a reference book, but I don't see how it is derived. I have
> been able to derive a result for the case in which X is only normal
> and not lognormal. That was the easier case since if X is normal then
> so is X-K.

Sounds like you are trying to derive the Black-Scholes formula. You
could consult one of the standard texts by John Hull.