#===========================================
# Figure 14.7.R.
# R script to simulate investment with randomly
# fluctuating prices many times and draw histogram
# of final prices.
#===========================================

# 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=numeric(mnts+1) # Vector to contain the log-prices.
t=x;              # Vector to contain the accumulated times.
log.prices=numeric(sim.num)

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

# Step 2. Plotting.
prices=exp(log.prices) # Change log-prices to prices.
hist(prices,freq=FALSE) # Histogram.