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Value-at-Risk and Extreme Returns
Jon Danielsson and Casper de Vries
Accurate prediction of the frequency of extreme events is of primary importance in many financial applications such as Value--at--Risk (VaR) analysis. We propose a semi--parametric method for VaR evaluation. The largest risks are modelled parametrically, while smaller risks are captured by the non--parametric empirical distribution function. The semi--parametric method is compared with historical simulation and the J. P. Morgan RiskMetrics technique on a portfolio of stock returns. For predictions of low probability worst outcomes, RiskMetrics analysis underpredicts the VaR while historical simulation overpredicts the VaR. However, the estimates obtained from applying the semi--parametric method are more accurate in the VaR prediction. In addition we study the role of an option that lowers the downside risk of the portfolio.