Evaluating Validity of Expected Shortfall Estimation Method in Measuring Market Risk for Bank's Trading Book Position

Abstract : Expected Shortfall (ES) has become a pivotal risk measure in financial regulation, particularly under the Basel III Fundamental Review of the Trading Book (FRTB), which replaces Value-at-Risk (VaR) due to ES’s ability to capture tail risk better. This study investigates the performance of two ES estimation methods—GARCH-t and Historical Simulation (HS)—in the context of foreign exchange (FX) against the IDR currency. Unlike VaR, ES incorporates the magnitude of extreme losses and is thus more sensitive to volatility dynamics. However, each estimation method presents trade-offs between responsiveness, robustness, and capital allocation. Using exchange rate data from 2007 to 2024, the ES values were computed under each method and validated through Acerbi–Szekely Z-tests on both tails. The backtesting results reveal that GARCH-t performs best during stress periods but demonstrates instability in calm markets. In contrast, Basic HS demonstrates more consistent backtest in the overall performance score across years. These findings offer practical insights into ES model implementation, emphasizing the importance of model selection, dual-tail backtesting, and supervisory alignment with FRTB.