Journal
JOURNAL OF MONEY CREDIT AND BANKING
Volume 39, Issue 7, Pages 1613-1649Publisher
WILEY-BLACKWELL
DOI: 10.1111/j.1538-4616.2007.00081.x
Keywords
financial risk management; value at risk; extreme value theory; skewed fat-tailed distributions
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This paper develops an unconditional and conditional extreme value approach to calculating value at risk (VaR), and shows that the maximum likely loss of financial institutions can be more accurately estimated using the statistical theory of extremes. The new approach is based on the distribution of extreme returns instead of the distribution of all returns and provides good predictions of catastrophic market risks. Both the in-sample and out-of-sample performance results indicate that the Box-Cox generalized extreme value distribution introduced in the paper performs surprisingly well in capturing both the rate of occurrence and the extent of extreme events in financial markets. The new approach yields more precise VaR estimates than the normal and skewed t distributions.
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