Proved the price's theorem

Well this is a horrible post:-) i have just got into University of Southern California and I am just learning some probability fundaes.

So here goes the hot news :-)))

I tried to prove price's theorem.

It was of course a very standard theorem.. so i could not help but look into how it was done.

It says this, If u have a normal distribution and a function g(x) which satisfies some conditions then the rate of change of the expectation of the function with respect to the variance is directly proportional to the expectation of the double differencial of the function with respect to x. eeeeks :-) :-0

all this stems from ONE fact. that the charectoristic function differential w.r.t variance is equal to frequency^2 times the charectoristic function itself. This means that we have the double differectial with respect to x in the x domain. This is interesting. we are converting the differencial in one variable into the differnencial of another. tooo gud.