Efficient Simulation of Brownian Motion in R -

data=data.frame(matrix(rnorm(1000*300,0,1),1000,300)) weiner.matrix=data.frame(cumsum(data))  mu=0 sigma=.15 dt=1/1000    bmot=data.frame(matrix(na,1000,300)     bmot[1,]=100     (j in 1:ncol(data)){     (i in 2:nrow(data)){        bmot[i,j]=bmot[i-1,j]*(1+mu*dt+sigma*sqrt(dt)*(weiner.matrix[i,j]-weiner.matrix[i-1,j]))      }     } 

i trying simulate matrix of 1000 rows , 300 columns, 300 variables of geometric brownian motion. initial value starts @ 100 , randomness kicks in periods after t=1/row=1.

is there way run 300 brownian motion simulation without going cell-by-cell have in loop??

you can use cumsum on set of normal variables produce single variable of brownian motion.

random <- rnorm(1000, 0, sqrt(0.15)) x <- 100 + cumsum(random) nsim <- 300 

you can use apply, for loop fast:

x <- matrix(rnorm(n = nsim * 1000, sd = sqrt(0.15)), nrow = 1000, ncol = 300) (i in 1:nsim) x[,i] <- cumsum(x[,i])