Exploring Alternative Distributions in Ito's Lemma for Financial Engineering

[Iforgot]

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.

 

[twofish-quant]

I think the variance of the distribution actually delta T. What is 1 is the volatility.

I don't have Hull in front of me, but what you say makes sense. Imagine mini-epsilon that could take a value of +mini-epsilon or -mini-epsilon. Now imagine that you iterate that a large number of steps so that you get epsilon. At that point, what you get is a normal distribution with variance of epsilon.

 

[ghouse099]

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