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\title{Derivatives Lab}
\author{Session 12}
\date{October 31, 2011}
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\def\e{\mathrm e}

\begin{enumerate}

\item Compute an ensemble of standard Brownian paths $W(t)$ over the
interval $[0,1]$.  Empirically determine mean and variance $W(1)$.

\item Compute an ensemble of geometric Brownian paths
\[
  S(t) = \exp((\mu - \tfrac12 \, \sigma^2)\, t + \sigma \, W(t))
\]
and compute mean and variance of $S(1)$.

\item Compute the corresponding stock price paths which
underlie the binomial tree model and compare your results with
Problem~2.

\item Use the paths so obtained in a Monte--Carlo valuation of a
European call option.  Compare your result against the Black--Scholes
price. 

\end{enumerate}


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