Since the 1980s, Value-at-Risk (VaR) assumes a central place in risk management and nowadays in different regulations. Both Solvency II and Bale III require the use of this risk measure to calculate capital requirement. This measure is now widely used and is part of risk managers' common language. However, it is not as simple as it seems.
For Value-at-Risk, as it is often the case with mathematical objects, the theoretical definition can (and should) be interpreted several ways in practice. One must be aware of the consequences of choosing one interpretation or the other.
This article compares several interpretations of the theoretical VaR. It highlights with concrete examples differences due to using one definition or the other. And these differences are not small enough to be ignored!
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