stock index simulation

Monchichi · February 22nd, 2007, 7:19 am

hi there,I am trying to value an option on a stock index but I haven't found nothing good so far in the internet regarding that topic. The problem is that I have written a little program in Matlab concerning this topic where I simulate the index with a geometric brownian motion but the results are just strange. can someone please give an idea on how to evaluate these things? Thank you very much.Best Regards

gjlipman · February 22nd, 2007, 7:23 am

Simulating it as a geometric brownian motion is probably first order reasonable - what is strange about the results you are getting? One useful diagnostic is to use your simulation to price a forward (or the expected final value) - does that give a reasonable value?

Monchichi · February 22nd, 2007, 7:51 am

Hi gjlipman, thank you very much for your answer. Well the problem that I have is that for example I simulate the DAX over a period of 5 years and the final results are in the 8000 points. Well, even though, DAX has reached 7000 points now, I think its not very reasonable to believe that it will be around 8000 points in 5 years. Or maybe I lack the experience in that field. I didn't quite understand your suggestion to price a forward. how would I do that? I am a newbie in that field. Thanks!

Blazes · February 22nd, 2007, 8:45 am

If you are simulating the forward price you would expect the average of your simulations to be approximately equal to the forward price. So in the case of the DAX the answer would be 7,000*exp((r-d)*5) where r is the 5 y zero rate (adjusted for continuous compounding) and d is the dividend yield.

Monchichi · February 22nd, 2007, 9:59 am

Ah okay thanks Blazes,I'll check that.Do you have any suggestions regarding the model?Do you find that appropriate?

Blazes · February 22nd, 2007, 10:33 am

What is the purpose of your simulation? Is it for pricing or VaR purposes? What alternatives do you have available? If you are looking to compute prices or VaR in this way the advantage it gives you over the analytical method is confined to instruments where an analytical solution is not available. The problem of the actual distribution having skew or kurtosis is not addressed so whether the model is OK or not depends on the purposes for which it is being used.

Monchichi · February 23rd, 2007, 12:02 pm

Well the purpose of my calculation is just for pricing. And up until now I don't have any other alternatives except geometric brownian motion simulation.thanks for your reply!!!

MrMartingale · February 23rd, 2007, 3:56 pm

There is lots of good information available on how to value an option.Look for a book by John Hull called Options, Futures and Other Derivatives.

jbott · February 26th, 2007, 3:59 pm

What Blazes said sounds right to me. You should get risk-neutral probabilities for each node of the tree so the end result is basically a forward price that's somewhere around the risk free rate of return (e.g, the 5 year zero rate).

Monchichi · March 1st, 2007, 8:24 am

Thank you very much everybody for your answers!