Not sure if I am asking the appropriate question(s) here, but here it goes anyway:Have implemented a very simple example of MS in excel for standard European call on F/X. Inceasing the number of sims (i.e. from 4,000 to 5,000 etc) and noting the proximity to BS value for same option and related variance. What specific tests should I consider to test for the statisical significance of the results.Also, when performing a simple linear regression and correlation on two variables, can someone confirm that it is never appropriate to perform the analysis on the changes in the levels of the indices/rates but only on the LN returns of the indices/rates (For example BMA (y) and 1M LIBOR (x) or spot GPB(x) and 3M Forward GBP(y)).Thanks in advance for he help

"Not sure if I am asking the appropriate question(s) here, but here it goes anyway:Have implemented a very simple example of MS in excel for standard European call on F/X. Inceasing the number of sims (i.e. from 4,000 to 5,000 etc) and noting the proximity to BS value for same option and related variance. What specific tests should I consider to test for the statisical significance of the results.Also, when performing a simple linear regression and correlation on two variables, can someone confirm that it is never appropriate to perform the analysis on the changes in the levels of the indices/rates but only on the LN returns of the indices/rates (For example BMA (y) and 1M LIBOR (x) or spot GPB(x) and 3M Forward GBP(y)).Thanks in advance for he help " Naive Monte Carlo Simulation unfortunately is far from the correct value(BS for your case) both as accuracy and precision (Standard error in approximation). I advise you to use some variance reduction techniques such as Control variate, anthitetic and importance sampling. Just look for these in goegle.Statistical tests; I think standard error you can use as precision and the correct price for accuracy.

You wroteAlso, when performing a simple linear regression and correlation on two variables, can someone confirm that it is never appropriate to perform the analysis on the changes in the levels of the indices/rates but only on the LN returns of the indices/rates (For example BMA (y) and 1M LIBOR (x) or spot GPB(x) and 3M Forward GBP(y)).This question has not correct answer, so lets seperate into two cases: financial (1) and econometrics (2). 1. If you are estimating parameters for a BS world pricing model, you will always perform your regresssion on the log returns.2. Any time series data whether levels or log returns may contain unit roots. Unit roots mean you have stochastic exongenous (RHS) variables causing problems with linear regression models. You should test for unit roots which most statistical software will but not excel. After testing for unit roots estimate the appropriate time series model. Good Luck

I am sorry, there is no any problem of unit roots when you generate lognormal model. Unit root problem arises in more advanced econometric time seris when return depends on the previos returns. It comes from disrete linear system theoyr whe is staded that the stable (not going to infinity) linear system shoud have of characteristic values into the unit circle. This is not the case of classical BS, where thereis no any lag dependence... Most probbably you have just a bug in your simulation. BS by MC is evaluated straightforwardly and you should see the convergence pretty fast. But what you have to check is the value of volatility in the simulation. Be sure that you normalize it correctly. For instancefactor 100 may destroy your simualtion completely (if you use vol=30 instead, 0.3 , etc)

df/F=mu dt + sigma dz.This is the BS lognormal SDE. df= F(t)-f(T-1). This model depends on past returns. In the continuous limit this is an AR(1) model in the price changes.