I have a function that I need to draw with R using a daily step of 1 for 3 years.
S(t)= S(0)exp(0.06t+0.20w(t)) #(1)
with S(0) =20
w(t) = standard Brownian movement
I am kinda blocked. I know this code should work but I don't know how to have the same length between my "t" and my w(t) length(t)=901 and length(w(t))=902. How to make them alike????
t <- seq(0,900,length=901)
length(t)
v = matrix(rnorm(log(20)+0.06*t,sd=sqrt((0.20)^(2)*t)))
z = matrix(NA, ncol=900, nrow=5)
w = function(t)
{c(0,cumsum(v))}
length(w(t))
Bn <-log(20)+ 0.06*t +0.20*w(t)
Br <- log(Bn)
plot(t,Br,type="l",xlab="Temps")
for (i in 1:5) # I need to draw 5 path of the function(1)
{z[i,] = c(0,cumsum(Br[i,]))}
dim(z)
u= apply(z,2,mean) #mean of the 5 path
plot(t,z[1,],xlab="temps",type="l",ylab="Movement Brownian")
for (i in 1:5){lines(t,z[i,])}
lines(t,u,lwd=2,col="red")
Please I need help. Thank you for your time.