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Ito's Lemma

  1. Aug 12, 2009 #1

    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?

    Last edited by a moderator: May 4, 2017
  2. jcsd
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