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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. |
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