Backtesting for the Expected Shortfall of the Trading Book: An Assessment of Methodologies
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Abstract
Due to the Crisis of 2008, the Basel Committee accelerated the process for update the Accord and identified some weaknesses such as the inability of VaR to capture the tail risk. Subsequently, it was recommended to substitute VaR, a non-coherent measure of risk due to the absence of subadditivity, by CVaR. This measure, while not being testable or elicitable, is at least conditionally elicitable and therefore also conditionally testable. To validate the CVaR models, simulations were made with the three Acerbi methods and another one suggested in this paper that adapted the Quantil Approximation. Of these four, none was perfect. The three Acerbi methodos had failures in some tests and the one suggested in this paper presented better results than the VaR Backtesting.
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