Extreme Value Theory and Value at Risk
AbstractValue 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 information. However, assets returns usually come from fat-tailed distributions. Therefore, computing VaR under the assumption of conditional normality can be an important source of error. We illustrate this point for some return series key to the Chilean financial market 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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Bibliographic InfoPaper provided by Centro de Economía Aplicada, Universidad de Chile in its series Documentos de Trabajo with number 154.
Date of creation: 2003
Date of revision:
Other versions of this item:
- Viviana Fernandez, 2003. "Extreme Value Theory and Value at Risk," Revista de Analisis Economico – Economic Analysis Review, Ilades-Georgetown University, Economics Department, vol. 18(1), pages 57-85, June.
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
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