#===========================================
# Figure 14.7 vectorized.R.
# R script to simulate investment with randomly
# fluctuating prices many times and draw histogram
# of final prices.
#
# An entire vector of log-prices is simulated
# each time-interval, and stored as a column in a
# matrix named x.  The final column of the matrix
# goes into the histogram.  The approach eliminates
# one of the for-loops in Figure 14.7.R.
#===========================================

# Step 0. Initialization.
days=60            # Time horizon of simulation (trading days).
sim.num=1000       # Number of simulations.
r=.06              # Annual average return of 6%.
dt=1/124800        # 124800 minutes in 260 8-hr trading days
                   # per year.
sig=.2*r*sqrt(dt)  # Spread constant for noise.
mnts=days*8*60     # Number of minutes in 60 trading days.
x=matrix(0,sim.num,mnts+1) # Matrix to contain the log-prices:
                           # every row is a different simulation,
                           # every column is a different time.
t=numeric(mnts+1); # Vector to contain the accumulated times.

# Step 1. Simulation.
w=matrix(rnorm(mnts*sim.num,0,sig),sim.num,mnts)
x[,1]=log(1000) # Initial investment amount.
t[1]=0 # Initial time.
for (i in 1:mnts) {
  dx=r*dt+w[,i]    # Vector of changes in log-price during one minute.
  x[,i+1]=x[,i]+dx # Vector of new prices after one minute.
  t[i+1]=t[i]+dt   # New accumulated time after one minute.
}

# Step 2. Plotting.
prices=exp(x[,mnts+1])  # Change log-prices to prices.
hist(prices,freq=FALSE) # Histogram.