Using approximate results for validating value-at-risk

Jimmy Hong, John Knight, Steve Satchell and Bernd Scherer

Abstract

ABSTRACT

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 efficacy of a VaR forecast. One such procedure that can be useful is the construction of confidence intervals. Failure of the forecasts to lie within their confidence 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 confidence 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 refinement. We also carry out some exact and Monte Carlo analysis to find the degree of approximation involved.