Hello,I am simulating a GBM in a Mote Carlo Simulation with VBA. I have the problem that my mean return from the simulated pathes is not corresponding to the exogenous mean return that I use for the simulation. I attached the code that i use. I am sure that the representation of the GBM is correct, nevertheless I always get a too small mean from the simulation. randoms is a vector that is normally distributed (0,1). stocks(i) = stocks(i - 1) * Exp((mean - 0.5 * (volatility ^ 2)) * time_increment + volatility * time_increment ^ 0.5 * randoms(i))to me it seems that the term 0.5 * (volatility ^ 2) automatically reduces the mean return. Still this representation is correct. Many thanks for help/explanation.F.

Hello,Your simulation seems fine allright, now how do you compute the mean return ?

i calculate ln(ST/St)/(T-t)this should be correct. when i use mean 0 and stdev of 30% i get hugely negative average returns ... must it be so with zero mean it reduces to Exp(( - 0.5 * (volatility ^ 2)) * time_increment + volatility * time_increment ^ 0.5 * randoms(i))with randoms mean zero it reduces to Exp(( - 0.5 * (volatility ^ 2)) * time_increment )---> smaller mean in the simulation

Well, from S_t = S_0 exp( (m - sigma^2 / 2) t + sigma W_t ) you derive: log ST / St = (m - sigma^2 / 2) (T - t) + sigma (W_T- W_t)Divide this by (T - t) and take the expectation ; you get (m - sigma^2 / 2) ; so it's only natural to get a negative value if m = 0. Right ?

you are right and i think i need to add (sigma^2 / 2) to the mean i get from the empirical distribution.strange i didnt see that topic discussed somewhere else. maybe it is too basic.thanks