Testing and comparing Value-at-Risk measures
Value-at-Risk (VaR) has emerged as the standard tool for measuring and reporting financial market risk. Currently, more than eighty commercial vendors offer enterprise or trading risk management systems which report VaR-like measures. Risk managers are therefore often left with the daunting task of having to choose from this plethora of risk models. Accordingly, this paper develops a framework for asking, first, how a risk manager can test that the VaR measure at hand is properly specified. And second, given two different VaR measures, how can the risk manager compare the two and pick the best in a statistically meaningful way? In the application, competing VaR measures are calculated from either historical or option-price based volatility measures, and the VaRs are tested and compared. La valeur exposée au risque (value at risk - VaR) est devenue un outil standard de mesure et de communication des risques associés aux marchés financiers. Plus de quatre-vingts fournisseurs commerciaux proposent actuellement des systèmes de gestion d'entreprise ou de gestion des risques commerciaux fournissant des mesures de type VaR. C'est donc souvent aux gestionnaires des risques qu'incombe la tâche difficile d'opérer un choix parmi cette pléthore de modèles de risques. Cet article propose un cadre utile pour déterminer par quel moyen le gestionnaire des risques peut s'assurer que la mesure de VaR dont il dispose est bien définie, et, dans un deuxième temps, comparer deux mesures de VaR différentes et choisir la meilleure en s'appuyant sur des données statistiques utiles. Dans l'application, différentes mesures de VaR sont calculées à partir soit de mesures de volatilité historiques ou de mesures de volatilité implicites dans le prix des options; les VaR sont également vérifiées et comparées.
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