Value-at-Risk (VaR)
The authors describe how to implement VaR, the risk measurement
technique widely used in financial risk management.

The historical simulation method is useful when the amount
of data is not very large and we do not have enough information
about the profit and loss distribution. It is usually
very time consuming, but its main advantage is that
it catches all recent market crashes. This feature is very
important for risk measurement.
The variance covariance method is the fastest. However
it relies heavily on several assumptions about the
distribution of market data and linear approximation of
the portfolio. It is probably the best method for quick estimates
of VaR. However one should be very careful when
using this method for a non-linear portfolio, especially in
the case of high convexity in options or bonds.
The Monte Carlo simulation method is very slow, but
it is probably the most powerful method. It is flexible
enough to incorporate private information together with
historical observations. There are many methods of speeding
calculations, so-called variance reduction techniques.
The results of all three methods are similar and our
goal was to demonstrate a very basic approach to risk
measurement techniques using Mathematica.