I'm working on a project which is requiring me to test Binomial option pricing on real data.
So far I have just been working with test data and my option pricing method works fine.
The issue I'm faced with now, is how to test my method on real data. The problem I have is that I have looked at historical prices for the assets that I'm trying to price the option of, to determine the volatility. I've then used Monte Carlo to price the option. Imagine that we find the volatility to be "X" and that corresponds to u = 1.1 and d = (1/u). Our optimal replication method will tell us how to delta hedge this option, but what if going into the future the actual underlying does not take on one of the values as predicted by the binomial model?
Consider the following example:
$110 / / $100 \ \ \ $90.90
What if the value at t=1 is actually \$120? Or if it remains at \$100? Should we just choose the one that is closest to the value? And if so, what do we do when the value remains the same? I could implement the trinomial case?