#source("C:/Documents and Settings/rolf/MathFin Fall03/EULER.GBM.R")
#source("EULER.GBM.R")

GBMdrift<-function(x,mu=0.1) {mu*x}
GBMvol<-function(x,sigma=0.1) {sigma*x}

Tmax<-10
Nsim<-1000
dt<-Tmax/Nsim
tvector<-dt*0:Nsim
dW<-sqrt(dt)*rnorm(Nsim)

X<-0:Nsim
X[1]<-1  	#vectors in R are unit-offset

mu<-0.1

par(mfrow=c(2,2))

for(j in 1:4){
sigma<-0.05*j

title<-paste("Geom. BM with \n mu =",round(mu,2), " and sigma =", round(sigma,2))


for(i in 1:Nsim) {X[i+1]<-X[i]+GBMdrift(X[i],mu)*dt+GBMvol(X[i],sigma)*dW[i]}
plot(tvector,X,type='l',xlab="t",ylab="X(t)",ylim=c(0,4),main=title)
points(tvector,X[1]*exp(mu*tvector), type='l', lty=2)
}