Trivial but very important

Yesterday we were working on an assignment problem on monte carlo simulation. In this we had to calculate the Stock price by simulation and then call and put option price. And later on find the 95% VaR on portfolio of stock and option. Now what was trivial thing . We were not getting the correct answers and suddenly someone saw that we had used riskfree rate in the stock price modeling not the mu . And then the discussion started that according to risk neutral world Stock price should have riskfree rate in the GBM equation . And all were thinking that wether it should be mu or riskfree rate. Though its very obvious that we should use mu(mean) not the riskfree rate in mdeling the stock price but sometimes you get confused. So once again I want to put down the same . You use riskfree rate in modelingin options only reason because you already have mu in Stock price . That is the risk free world. Not that you use riskfree rate in Stock price . Had that been the case all stocks would have same drift and just different volatility . That only means that High growth companys stock would never rise which have high mean (expected growth rate).