# Ito's Lemma

Hi,

I am studying brownian motion and the Black-Scholes formula.

Our problem assumes that
1. Stock returns follow a normal distribution
2. Based on #1 the stock price follows a lognormal distribution because y = exp(X) is lognormal if X is normally distributed. Here the stock prices are continuously compounded.

3. So I would expect that the stock return would have an average return of "u" because this is the average value of a normal distribution... but it is actually "u - p^2/2".

p = standard deviation
http://www.bionicturtle.com/learn/article/lognormal_distribution_part_3_future_stock_price/ [Broken]

From what I am gathering this is because Ito's lemma tells us that...

St = So * Exp ( u - p^2 / 2 )*t + pWt

So why dont the two match?

I am having trouble following the proof and "repercussions" of the ito theorem. I tried wiki for ito's lemma but it is very confusing.

Are there any beginners info that I could use to get a better grip of this concept? Like books or online or can you explain any of this?

Thanks

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