[R] simple loop problemo (Geo brownian motion)

[Duncan Murdoch]

On 19/11/2010 1:09 PM, newbster wrote:
> I would like to plot multiple random walks onto the same graph.  My p
> variable dictates how may random walks there will be.
>
>
> par(mfrow=c(1,1))
> p<- 100
> N<- 1000
> S0<- 10
> mu<- 0.03
> sigma<- 0.2
> nu<- mu-sigma^2/2
> x<- matrix(rep(0,(N+1)*p),nrow=(N+1))
> y<- matrix(rep(0,(N+1)*p),nrow=(N+1))
> t<- (c(0:N))/N
> for (j in 1:p)
> {
> z<- rnorm(N,0,1)
> x[1,j]<- 0
> y[1,j]<- S0
> for (i in 1:N)
> {
> x[i+1,j]<- (1/sqrt(N))*sum(z[1:i])
> y[i+1,j]<- y[1,j]*exp(nu*t[i+1]+sigma*x[i+1,j])
> }
>
> plot(t,y,type="l",xlab="time", ylab="Geometric Brownian motion")
>
> }
>
>
> Any help would be appreciated, thanks.
>

You can use the matplot function to plot multiple columns of a matrix at 
once.  So with your code as above, leave out the call to plot(), then  
matplot(t, y) would give you approximately what you're looking for 
(though the colour and symbol choices need some work).

You can get rid of the inner loop by using cumsum() and vectorized 
calculations; then it will be reasonably fast.

Another way to do this is to create the plot before the loop, then use 
lines() to add lines to it within the loop.  Then you need to guess the 
scale ahead of time, or do a little experimentation.

Duncan Murdoch