[R] simple loop problemo (Geo brownian motion)

2010-11-19 Thread newbster 

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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Re: [R] simple loop problemo (Geo brownian motion)

2010-11-19 Thread 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

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Re: [R] simple loop problemo (Geo brownian motion)

2010-11-19 Thread Yihui Xie 
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 xieyi...@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 gpm8...@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.

 __
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 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.


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and provide commented, minimal, self-contained, reproducible code.