1

Here is the current script I have: 

delta <- 1/52
T <- 0.5
S0 <- 25
sigma <- 0.30
K <- 25
r <- 0.05
n <- 1000000
m <- T/delta
S <- numeric(m + 1)
S[1] <- S0
#Payoff asian option
asian_option_price <- function() {
  for(j in 1:m) {
    W <- rnorm(1)
    S[j + 1] <- S[j] * exp((r - 0.5 * sigma^2) * delta + sigma * sqrt(delta) * W)
  }
  Si.bar <- mean(S)
  exp(-r * T) * max(Si.bar - K, 0)
}
#Loops
C <- raply(n, asian_option_price(), .progress = "text")

My issue is that I need to use "-W" for a second simulation right after this one is done. The way the script is made, "W" is inside my loop which makes it impossible (i think) to use the corresponding "-W" after that. I think I need to use an independent matrix filled with rnorm() mat(x) = matrix(rnorm(m*n,mean=0,sd=1), m, n) so that I can simply use -mat(x) in my second simulation. I don't get how to take "W" out of my loop and still use it's corresponding matrix. Any help would be very useful. Thanks!

Jeremi
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1 Answers1

0

Your idea to preallocate all the random numbers is correct. You could then loop over the individual entries. However, it is faster to go for a vectorized approach:

delta <- 1/52
T <- 0.5
S0 <- 25
sigma <- 0.30
K <- 25
r <- 0.05
n <- 100000
m <- ceiling(T/delta)

W <- matrix(rnorm(n*m), nrow = m, ncol = n)
S <- apply(exp((r - 0.5 * sigma^2) * delta + sigma * sqrt(delta) * W), 2, cumprod)
S <- S0 * rbind(1, S)

Si_bar <- apply(S, 2, mean)
mean(pmax(Si_bar -K, 0)) * exp(-r*T)
Ralf Stubner
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