File:Euler Maruyama example.svg

Summary[edit]

R source:

brown <- function(N=100, dim=1, Tmax=1.0) 
{
  A <- apply(matrix(rnorm(N*dim), N, dim), 2, cumsum)
  ts(rbind(0, sqrt(Tmax/N)*A), start=0, deltat=Tmax/N)
}

set.seed(345087)

N <- 1000
m <- 10
W <- brown(N)
S <- exp(W - 0.5*time(W))
Shat <- ts(S[1], start=0, end=1, freq=N/m)
dW <- diff(W[seq(1,N+1,m)])
for (i in 1:length(dW)) {
  Shat[i+1] <- Shat[i] + Shat[i]*dW[i] 
}

svg()
plot(S, xlab="t", ylab="S")
lines(Shat, col="red", lwd=2)
dev.off()

Licensing[edit]

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