An Empirical Study: Expected Shortfall Estimation Methods for a Bank's Trading Book

Sammanfattning: This thesis investigates methods that estimate the Expected Shortfall correctly by passing the Acerbi-Szekely (2014) backtest in both stressed and calm periods. This backtest is added to in this thesis to test against both under- and overestimation of ES. This research is relevant due to the recent shift in the Basel’s Fundamental Review of the Trading Book from using Value-at-Risk as the leading risk measure to ES. The tests are performed on five hypothetical portfolios, which represent weighted asset classes and options hold in an actual bank’s trading book. The tested methods are a result of the literature reviewed; namely: Normal distribution, Student’s t-distribution and skewed Student’s t-distribution, each with both constant volatility and GARCH(1,1), BHS and VWHS with GARCH(1,1), as a filtered form of BHS. From a quantitative analysis, the result of this study indicates that the method with Student’s t-distribution with GARCH volatility performed superior throughout both periods compared to the other methods. Secondly, the in literature supported approach of VWHS with GARCH correctly estimated ES. In particular for the calm period, the Normal distribution with constant volatility received non-rejections for four out of six tested years. An interesting result to emerge from this study is the dependence between in-sample periods and the testing year regarding the degree of similarity in the level of standard deviation, which is of great influence across all methods’ test statistic results.