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.
I found the following demonstration of a skewed Galton board which results in a lognormal distribution here:
It is described in this article too (p. 343): http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf
I think that - if anywhere - Ito's lemma/correction term must hide here. But this has to be made exact!