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We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot be...
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We propose independence and conditional coverage tests which are aimed at evaluating the accuracy of Value-at-Risk (VaR) forecasts from the same model at different confidence levels. The proposed procedures are multilevel tests, i.e., joint tests of several quantiles corresponding to different...
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1 Introduction -- 2 Motivation -- Part I MEASURES -- 3 Basic Terms and Notation -- 4 Historical Value-at-Risk -- 5 Sensitivities -- 6 Stress Tests -- 7 Analytical Value-at-Risk -- 8 Expected Shortfall -- 9 Model Choices -- 10 A Monte Carlo Modi cation -- 11 Support Measures -- Part II OPERATIONS...
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