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The Value-at-Risk Measure

This chapter completes the preceding chapters with the calculation of VaR in very simple cases. The purpose is to provide a preliminary view of the VaR modeling framework, without getting into the technicalities of actual VaR models, and to show that the VaR concept applies to different risks. A first simplification is that we only consider the standalone risk of a transaction or a firm, without considering portfolio effects. Another simplification is that we assume that VaR is driven by a single factor, while the actual VaR model depends on a large number of factors. VaR models are expanded on in Section 10 for market risk and in Section 12 for credit portfolios.

Any VaR modeling starts from percentiles of the distribution of the target value. Accordingly we detail the percentile measure in the first section of this chapter. For market risk, the relevant distribution is that of normally distributed returns of linear instruments. The second section details the process for determining the VaR of a standalone "elementary position" that depends on a single risk factor. This section shows the sequence of steps leading to VaR by combining the previous risk measures, sensitivity and volatility. Value percentiles can also apply to the firm value. Any adverse variation of the firm value can be seen as impairing its solvency and credit standing. The final section shows how VaR for credit risk can be developed for a standalone firm. The methodology is a much simplified view of credit risk VaR in that we do not expand either the details of the Merton model (see Chapter 46) that inspires this example, or portfolio effects.

MODELING POTENTIAL VARIATIONS AND PERCENTILES

Because risks are always potential adverse deviations of earnings or of losses, defining "potential" variations is a common module of most risk models. Notably, VaR is the upper bound potential loss not exceeded with some predetermined low probability, called a confidence level.

 
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