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Tail Risk of VaR and Expected Shortfall
Multivariate Extreme Value Theory
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asset returns assume Bank of Japan bivariate exceedances bivariate extreme value confidence level convolution theorem dependence structure disregard distribution of exceedances distribution tail Embrechts emerging economies empirical distributions estimation Excess a Threshold Expected Shortfall 95 extreme loss extreme value copula extreme value distribution extreme value theory fat-tailed properties Figure Frank copula full dependence Gaussian Gaussian and Frank Gaussian copula Gumbel copula Hefferman Hiroshi Fujiki Indonesia Rupiah large losses Ledford and Tawn Left Tail Long-Term Capital Management loss distribution Malaysia Ringgit marginal distribution parameters market stress Mikosch million simulations Monetary Policy multivariate exceedances multivariate extreme value Pareto distribution Philippines Peso potential for large quantile Right Tail Risk Management Risk Measurement risk of expected scale parameter Shigenori Shiratsuka shortfall are calculated shortfall has tail Singapore Dollar Spearman's rho Spearman's rho=0.8 specific copula sub-additive Table tail indices tail probability tail risk Thailand Baht Threshold VaR 95 univariate Yamai and Yoshiba