Estimating Expected Shortfall Using Parametric and Non-Parametric Approaches

Abstract: With the implementation of the Fundamental Review of the Trading Book in January of 2022, financial institutions will be obligated to implement Expected Shortfall as a means of determining market risk capital. With the transition from Value at Risk to Expected Shortfall, the question of how to accurately forecast Expected Shortfall arises. This paper investigates the forecasting ability of non-parametric and parametric approaches used for estimating Expected Shortfall. More specifically, the paper considers, Basic Historical Simulation, Age-Weighted Historical Simulation, Volatility- Weighted Historical Simulation as well as parametric models based on a Normal distribution, t-distribution and on Extreme Value Theory. As a number of previous studies have investigated the ability of various estimation approaches’ ability not to underestimate market risk, the concept of overestimation of risk is introduced. The empirical results indicate that while the conditional Peaks Over Threshold approach yields the most satisfactory results when only underestimation is of a concern, the Volatility-Weighted Historical Simulation most accurately forecasts Expected shortfall when the concept of overestimation is introduced.