Using approximate results for validating value-at-risk

Incisive Financial Publishing Limited
Publication Type:
Journal Article
Journal of Risk Model Validation, 2010, 4 (3), pp. 69 - 81
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The failure of value-at-risk (VaR) methods in recent times has reawakened interest in its statistical properties. It is clear that we need quite general methods to assess the ef?cacy of a VaR forecast. One such procedure that can be useful is the construction of con?dence intervals. Failure of the forecasts to lie within their con?dence intervals in an ex-post sense is an indication of model failure. Under general assumptions, we derive asymptotic results for VaR which can be used to construct con?dence intervals. Our results indicate why VaR may be more accurately measured if the data is positively skewed and less accurately measured if the data is leptokurtotic. Previous approaches have been based on the assumption of normality and so the approximate approach defended by Jorion (1996, 2001) and Chappell and Dowd (1999) may need re?nement. We also carry out some exact and Monte Carlo analysis to ?nd the degree of approximation involved.
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