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.
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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
Maybe you can consider the brownian.motion() function in the animation package, e.g. library(animation) ani.options(interval = 0.05, nmax = 150) brownian.motion(pch = 21, cex = 5, col = "red", bg = "yellow", main "Demonstration of Brownian Motion") Or here is another (awkward) example of several "parallel" groups of random walks: https://github.com/hadley/ggplot2/wiki/Using-ggplot2-animations-to-demonstrate-several-parallel-numerical-experiments-in-a-single-layout Regards, Yihui -- Yihui Xie <xieyihui at gmail.com> Phone: 515-294-2465 Web: http://yihui.name Department of Statistics, Iowa State University 2215 Snedecor Hall, Ames, IA On Fri, Nov 19, 2010 at 12:09 PM, newbster <gpm8342 at yahoo.com> 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. > > > -- > View this message in context: http://r.789695.n4.nabble.com/simple-loop-problemo-Geo-brownian-motion-tp3050762p3050762.html > Sent from the R help mailing list archive at Nabble.com. > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >