R code for Ornstein-Uhlenbeck process

Question

Can any one help me with some R code to run Ornstein-Uhlenbeck process?

Answer 1

The code of Euler Maruyama simulation method is pretty simple (nu is long run mean, lambda is mean reversion speed):

ornstein_uhlenbeck <- function(T,n,nu,lambda,sigma,x0){
  dw  <- rnorm(n, 0, sqrt(T/n))
  dt  <- T/n
  x <- c(x0)
  for (i in 2:(n+1)) {
    x[i]  <-  x[i-1] + lambda*(nu-x[i-1])*dt + sigma*dw[i-1]
  }
  return(x);
}

Answer 2

Take a look at the sde package; specifically the dcOU and dsOU functions. You may also find some examples on the R-SIG-Finance mailing list, which would be in the results of a search on www.rseek.org.

Answer 3

You can also use the Sim.DiffProc package.

Have a look at this document:
Sim.DiffProc: A Package for Simulation of Diffusion Processes in R

See esp. chapter 2.1.2

There is even a Graphical User Interface (GUI) available for some functions:
http://cran.r-project.org/web/packages/Sim.DiffProcGUI/index.html

See chapter 4 in the above document for details.