Extreme Value Theory and Value at Risk

Authors

Keywords:

value at risk, extreme value theory, GARCH models, fat tails, market risk

Abstract

Value at Risk (VaR) is a measure of the maximum potential change in value of a portfolio of financial assets with a given probability over a given time horizon. VaR became a key measure of market risk since the Basle Committee stated that banks should be able to cover losses on their trading portfolios over a ten-day horizon, 99 percent of the time. A common practice is to compute VaR by assuming that changes in value of the portfolio are normally distributed, conditional on past in-formation. However, assets returns usually come from fat-tailed distri-butions. Therefore, computing VaR under the assumption of conditional normality can be an important source of error. We illustrate this point with Chilean and U.S. returns series by resorting to extreme value theory (EVT) and GARCH-type models. In addition, we show that dynamic estimation of empirical quantiles can also give more accurate VaR estimates than quantiles of a standard normal.

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References

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Published

2003-04-30

How to Cite

Fernandez, V. (2003). Extreme Value Theory and Value at Risk. Economic Analysis Review, 18(1), 57–85. Retrieved from https://www.rae-ear.org/index.php/rae/article/view/24

Issue

Vol. 18 No. 1 (2003)

Section

Articles

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Copyright (c) 2003 Viviana Fernandez

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