Backtesting para o Expected Shortfall do Trading Book: avaliação e análise das metodologias

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 V aR to capture the tail risk. Subsequently, it was recommended to substitute V aR, a non-coherent measure of risk due to the absence of subadditivity, by CV aR. However, in 2011 the absence of elicitability for CV aR was shown and this has led some people to believe that it is impossible to perform a backtesting for this risk measure. Elicitability is an mathematical property for model selection and not for validation, although the convexity of its scoring function is required for backtesting. It is important to know the identifiability and testability, which have a relation with elicitability. For a good backtesting in the Trading Book, the testable function must be sharp, which is strictly increasing and decreasing with respect to the predictive and realized variables, respectively, and meet the requirement of ridge backtest, which depends on the least possible V aR. The CV aR, while not being testable or elicitable, is at least conditionally elicitable and therefore also conditionally testable. To validate the CV aR models, simulations were made with the three Acerbi methods, two of this study for testing and another adapted from the quantile approximation. Of these six, none were perfect, but two presented better results than the V aR Backtesting. This study analyzed the risk measures V aR and CV aR by the Historical Simulation, Delta-Normal, Correlated Normal, Monte Carlo and Quasi-Monte Carlo Simulation methods in the 95%, 97.5% and 99% for the Brazilian bond and stock portfolios, as well as the Brazilian Real against the Dollar, Euro and Yen currencies, and used some backtesting for the two measures. This study also proposed a method to improve Backtesting results of V aR.