For loop in R (Special Case: Wiener Process) - r

Question

I'm dealing right now with a valuation of Option prices for my university thesis.
We need to program some things in R. It's the first time I'm working with a programming software like R. I've been doing this for the last 2 weeks and this is where I went so far:
s <- 120
#Value of the stock today
sd <- 0.1
#standard deviation
d <- 0.003
#Drift
N <- 365
T <-1
dt <-T/N
t <- seq(0,T, length=N+1)
W <- c(0, cumsum(sqrt(dt)*rnorm(N)))
#plot( t, W, type="l", main="Wiener process", ylim=c(-1,1))
S <- s*exp(d+sd*W)
S
This is a simple generalized Wiener process which I want to turn into a Monte Carlo simulation.
For S there are now 366 (N+1) Values of the Stock path. What I need is a "for loop" which takes the last Value of S and allocates it into a vector (list vector), so that I can run the loop for example 10000 times, collect every last Value of S and get the average of the vector.
I have no idea how I can program such a for loop.
I would really appreciate if you could help me or give me some good hints.
Greetings from Germany
Christian

Answer 1

I never studied Wiener Processes, but I think this would be a simple outline of the code you're trying to achieve:
stock_prices <- s #Initialise vector of stock prices
numIter <- 10^4 #Set number of iterations in the for loop
for(i in 1:numIter) {
s <- stock_prices[i] #This is the current stock price (for ith iteration / time step)
#Calculate the next stock price here, call it next_price
#Add price of next iteration / time step to your vector:
stock_prices <- c(stock_prices, next_price)
}
stock_prices will be a vector of the 10,000 stock prices you simulated.
I don't know how you calculate the next stock price from S, but if you draw from the values of S randomly, then it might be useful to check out the function sample (type ?sample for help on it).
Hope that helps

Answer 2

If you just want to run code repeatedly, putting it in a function is nice (but not absolutely necessary). I will refer to all the code in your question as <your code>.
To make a function that runs your code,
my_function = function() {
<your code>
}
The function will, by default, return its last line, in this case S. You only want the last element of S, tail(S, 1). So we can modify the function to return only that:
my_function = function() {
<your code>
return(tail(S, 1))
}
We can then call it in a for loop n times and assign the result. It is best to pre-allocate the vector for the results so that an appropriately sized block of memory can be set aside for it up front:
n = 10000
results = rep(NA, n)
for (i in 1:n) {
results[i] <- my_function()
}
This is equivalent to
n = 10000
results = rep(NA, n)
for (i in 1:n) {
<your code>
results[i] <- tail(S, 1)
}
And, for that matter, it is also equivalent to
results = replicate(n, my_function())
which is a handy shortcut.
If you want to be fancy, you could parameterize your function:
my_nice_function = function(s = 120, sd = 0.1, d = 0.003, N = 365) {
T <- 1
dt <- T / N
t <- seq(0, T, length = N + 1)
W <- c(0, cumsum(sqrt(dt) * rnorm(N)))
S <- s * exp(d + sd * W)
return(tail(S, 1))
}
Now my_nice_function has default values as in your code, but you can easily adjust them, e.g., to run the 50 simulations with sd = 0.2 you can do this:
replicate(50, my_nice_function(sd = 0.2))