For any financial engineers here who understand Hull's derivative pricing book. I've gone through chapter 12 (Wiener Processes and Ito's Lemma, 2008 edition). The derivation of Ito's lemma assumes epsilon is normally distributed with a mean of zero and a variance of 1. I have a hard time filling in steps with this assumption. Would the derivation also work if epsilon was a random variable that could take on only values of +1 or -1 with 50-50 probability? It would make the filling in steps much easier.