Hi Could somebody please summerize the role of the lemma in Black Scholes derivation. I know the derivation but am not fully happy with my understanding of the latters role!!!

Put simply,Standard calculus gives us a tools to find out how a function changes for a given change in some variable(s). However, when we have a function that contains a stochastic element (i.e. a brownian), how will the function now change for a given move in some underlying? Ito's lemma give us a tool to correct for the randomness in the function to derive an expression for a change in our function. As it happens, this correction takes the form of a taylor expansion that makes life a little easier.Rgds,R.

particularly as you don't need it - results on expected values of random variables with normal and lognormal distributions will get the BS formula

It depends on which derivation you're referring to. In the typical PDE derivation of the B-S formula Ito is needed to derive an SDE for the derivative (and then the corresponding PDE). Alternatively, in the Martingale derivation you need Ito to solve the SDE for the stochastic process describing the underlying. There is indeed one way to get away without Ito for stock options: you evaluate the expected value of the payoff for an arbitrary drift and then use Put-Call parity to find the correct (no arbitrage) drift. But this is particular to the case of an equity option. What Ito gives you is a coherent and elegant way to define a calculus for processes derived from brownian motion (as ordinary calculus simply does not work here).

in 99.99 percent of the cases ( and i think BS falls in this class)ito's lemms has the standard use of converting SDE into PDEin BS, we finally are able to get diffusion equation by using lemma..hope it helps!

all i was trying to point out was that if you start from pricing an option as the expected value of its payoff then all you need are expected values of normal and lognormal random variables - just an alternative way to think about BS rather than the original risk-free hedge portfolio and Ito's lemma

yes you are right, proving BS doesn't require one to know ito