Different Results Monte Carlo and Black-Scholes - where is my mistake?

Question

as an exercise, I am trying to simulate the BS model via Monte Carlo Simulation in R to price a normal European-style call option. However, the code will give me results that are way higher than the BS results even in case of 100,000 simulations. Here is my Code:

nSim=1000
T=5
N=T*360
K=7589.42
r=0.0219
Y0=7846.33
dt=T/N
drift=0.0
sigma=0.197
a=1
b=1

callOptionPrice=simulateCall()
callOptionPrice

  simulateCall=function(){
  C<-vector(mode="double",nSim)
for(a in 1:nSim){
 V=newPath()
 C[a]=max(V[N]-K,0)
  a=a+1    
  }
call=1/nSim*sum(C)*exp(-r*T)
return(call)
}

newPath=function() {
  Y<-vector(mode="double", length=N)
  i=0
  t=1
  Y[1]=Y0
  for(i in 0:N){
    dW=sqrt(dt)*rnorm(1)
    Y[t+1] = Y[t] + r*Y[t]*dt + sigma*Y[t]*dW
    t=t+1
  }
  return(Y)
}

Could anybody help me to find the mistake here? The actual result according to BS should be 1864.1388, however my code always returns numbers >2400.

Thank you in advance!

Answer 1

I've cleaned up your code a bit:

nSim=1000
T=5
N=T*360
K=7589.42
r=0.0219
Y0=7846.33
dt=T/N
drift=0.0
sigma=0.197

  simulateCall=function(){
  C<-vector(mode="double",nSim)
for(a in 1:nSim){
 V=newPath()
 C[a]=max(V[N]-K,0)    
  }
call=1/nSim*sum(C)*exp(-r*T)
return(call)
}

newPath=function() {
  Y<-vector(mode="double", length=N)
  Y[1]=Y0
  for(i in 1:(N-1)){
    dW=sqrt(dt)*rnorm(1)
    Y[i+1] = Y[i] + r*Y[i]*dt + sigma*Y[i]*dW
  }
  return(Y)
}

callOptionPrice=simulateCall()
callOptionPrice

Check where I made changes, some stuff you put in there was useless like specifying the variable you loop over and adding code within the loop to increment that variable. Or defining superfluous variables.