Chapter 8.P2, Problem 2P

Simulate five sample trajectories of Eq. (1) for the following parameter values and plot the trajectories on the same set of coordinate axes: $\mu =0.12,\sigma =0.1,T=1,s=\$40,N=254$. Then repeat the experiment using the value $\sigma =0.25$ for the volatility. Do the sample trajectories generated in the latter case appear to exhibit a greater degree of variability in their behaviour?

Hint: For the ${\epsilon }_n\text{'s}$, it is permissible to use a random number generator that creates normally distributed random numbers with mean zero and variance $1$.

$S_{n+1}=S_n+\mu S_n\Delta t+\sigma S_n{\epsilon }_{n+1}\sqrt{\Delta t},S_0=s$, (1)