I am trying to do a MC simulation for some options that i have priced with BSM. I want to change the volatility of the underlying and observe the changes in the option price. The problem is the volatility does not follow any distributions due to the volatility clustering effect. So I don't know how to trick the distribution (I am using Excel Sim) Can anyone please help?

QuoteOriginally posted by: ileanaI am trying to do a MC simulation for some options that i have priced with BSM. I want to change the volatility of the underlying and observe the changes in the option price. The problem is the volatility does not follow any distributions due to the volatility clustering effect. So I don't know how to trick the distribution (I am using Excel Sim) Can anyone please help?Your question seems confusingly phrased to me, but I will give it a shot as no replies. First, I think we need a translation before you can get sensible replies. Here is mine:"I want to simulate a daily volatility process by making independent draws each day from some volatility distribution.But, this will be counter-factual as real-world volatilities 'cluster' (are auto-correlated) and mine won't be.How can I get volatility clustering into what I am doing?"Is that about right?

Yes, that seems about right, thank you for responding

... "cluster MC" topic?

QuoteOriginally posted by: ileanaYes, that seems about right, thank you for respondingSo, off-hand, a simple vol. dependency structure could be to take a weighted sum of your last daily draw and a new independent draw.

Could I ask what your purpose of running the MC is?Be aware of the risk measure used. - For risk purpose (e.g., VAR), people tends to use real measure as you're trying to find what will happen for your un-hedged position. But some people prefers using risk neutral measure.- For pricing purpose (e.g., option pricing), it's almost a must to use risk neutral measure in order to get rid of arbitrage. In other words, you should use implied volatility unless you have very strong reason not to be.To monitor volatility risk, I would propose using vega risk measure or generating risk matrix for various spot / vol combinations.

Calibrate a GARCH(1,1) model then simulate different paths? The relevant functions are garchfit() and garchsim() in Matlab, I believe.