I am trying to devellop a small option pricer using win32 API. To do that I use monte carlo simulation to compute the price of a call option but there is a mistake in my simulation and I don't see where. Someone can tell me why the two prices are different ?

The price for a call with the black and scholes formula is 6.84 but the one given by the monte carlo simulation is 7.54. (There is no error in the price from the black and scholes formula)

This is the code :

std::vector<double> vecteur_pas(double T) {
std::vector<double> pas;
pas.push_back(0);
double x = T / nb_pas;
for (int i = 1; i <= nb_pas; i++) {
    pas.push_back(pas[i-1] + x);
}
return pas;


std::vector <double> NormalRnd() {
std::vector <double> brow;
brow.push_back(0);
double unif_1, unif_2;
for (int i = 0; i < nb_pas; i++) {
    unif_1 = (double(rand() + 0.5)) / (double(RAND_MAX) + 1.0);
    unif_2 = (double(rand() + 0.5)) / (double(RAND_MAX) + 1.0);
    brow.push_back(sqrt(-2 * log(unif_1)) * cos(2 * M_PI * unif_2));
}
return brow;



std::vector<double> MBG(double S, double mu, double vol, double T) {
std::vector<double> traj;
traj.push_back(S);
std::vector <double> b =NormalRnd();
std::vector<double> pas = vecteur_pas(T);
double drift = 0.0;
double diffusion = 0.0;
for (int i = 1; i <= nb_pas; i++) {
    drift = (mu - 0.5 * pow(vol, 2)) * (pas[i]-pas[i-1]);
    diffusion = vol * b[i] * sqrt(pas[i] - pas[i - 1]);
    traj.push_back(traj[i - 1] * exp(drift + diffusion));
}
return traj;

The MBG function is called in a loop after :

for (int i = 0; i < 100000; i++)
        {
            if ((i % 1000) == 0)
            {
                SendDlgItemMessage(Calcul, IDE_PB, PBM_STEPIT, 0, 0);
            }
            vector<double> proc_prix = MBG(actif.S, actif.r, actif.v, actif.T);
            double last_value = proc_prix[proc_prix.size() - 1];
            Prime = Prime + std::max(last_value - actif.K, 0.0);
        }
        Prime = Prime / 100000;

This is the output