# Demonstration of Ito's correction term/lemma in binomial tree

I am preparing an undergraduate QuantFinance lecture. I want to demonstrate the ideas of Ito's correction term and Ito's lemma in the most accessible manner.

My idea is to take the "working horse" of Quantitative Finance, the binomial model and demonstrate both concepts there. Unfortunately I haven't found any references and am encountering unanticipated difficulties myself in combining both views.

When these concepts can be found in the continuous version they must be hiding in the discrete version too - can anybody please demonstrate them this way or give some reference.

EDIT
I found the following demonstration of a skewed Galton board which results in a lognormal distribution here:

I think that - if anywhere - Ito's lemma/correction term must hide here. But this has to be made exact!

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@Mark Joshi: Would you like to take a stab at it? I would love to see your answer here! –  vonjd Feb 27 at 6:35

But the more you get to the limiting case of your binomial tree (which is the continuous case) it must show up somewhere - as it shows up in the simulation in the paper the more randomness you include in your process (increasing $\sigma$). It shows up in the sense that it is different compared to the non-random case and in the choice of the endpoint (left=Ito) of the intervals. –  vonjd Jan 25 '12 at 18:16