#===========================================
# Figure 14.6.R.
# R script to simulate investment with randomly
# fluctuating prices.
#===========================================

# Step 0.  Initialization.
days=60             # Time horizon of simulation (trading days).
r=.06               # Annual average return of 6%.
dt=1/115200         # 115200 minutes in 240 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.
x[1]=log(1000)      # Initial investment amount.
t[1]=0              # Initial time.

# Step 1.  Simulation.
w=rnorm(mnts,0,sig) # Generate vector of normal noises outside
                    #  the loop (more efficient)
for (i in 1:mnts) {
  dx=r*dt+w[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.
}

# Step 2.  Plotting.
n=exp(x)            # Change log-prices to prices.
plot(t,n,type="l")  # Plot prices vs time.