MCS for single and multi assets

#  MCS for single and multi assets

asset.paths <- function(s0, mu, sigma, 
                        nsims = 10000, 
                        periods = c(0, 1)	# time periods at which to simulate prices
) 
{
  s0 = as.vector(s0)
  nsteps = len(periods)
  dt = c(periods[1], diff(periods))
  
  if( len(s0) == 1 ) {
    drift = mu - 0.5 * sigma^2
    if( nsteps == 1 ) {
      s0 * exp(drift * dt + sigma * sqrt(dt) * rnorm(nsims))
    } else {
      temp = matrix(exp(drift * dt + sigma * sqrt(dt) * rnorm(nsteps * nsims)), nc=nsims)
      for(i in 2:nsteps) temp[i,] = temp[i,] * temp[(i-1),]
      s0 * temp
    }
  } else {
    require(MASS)
    drift = mu - 0.5 * diag(sigma)
    n = len(mu)
    
    if( nsteps == 1 ) {
      s0 * exp(drift * dt + sqrt(dt) * t(mvrnorm(nsims, rep(0, n), sigma)))
    } else {
      temp = array(exp(as.vector(drift %*% t(dt)) + t(sqrt(dt) * mvrnorm(nsteps * nsims, rep(0, n), sigma))), c(n, nsteps, nsims))
      for(i in 2:nsteps) temp[,i,] = temp[,i,] * temp[,(i-1),]
      s0 * temp
    }
  }
}




###############################################################################
# Load Systematic Investor Toolbox (SIT)
# https://systematicinvestor.wordpress.com/systematic-investor-toolbox/
###############################################################################
setInternet2(TRUE)
con = gzcon(url('http://www.systematicportfolio.com/sit.gz', 'rb'))
source(con)
close(con)

#*****************************************************************
# Plot some price paths
#******************************************************************  
S = c(100,105)
X = 98
Time = 0.5
r = 0.05
sigma = c(0.11,0.16)
rho = 0.63
N = 10000

# Single Asset for 10 years
periods = 0:10
prices = asset.paths(S[1], r, sigma[1], N, periods = periods)

# plot
matplot(prices[,1:100], type='l', xlab='Years', ylab='Prices',
        main='Selected Price Paths')


# Multiple Assets for 10 years
periods = 0:10
cov.matrix = sigma%*%t(sigma) * matrix(c(1,rho,rho,1),2,2)
prices = asset.paths(S, c(r,r), cov.matrix, N, periods = periods)

# plot
layout(1:2)
matplot(prices[1,,1:100], type='l', xlab='Years', ylab='Prices',
        main='Selected Price Paths for Asset 1')
matplot(prices[2,,1:100], type='l', xlab='Years', ylab='Prices',
        main='Selected Price Paths for Asset 2')