Backtesting Expected Shortfall : A qualitative study for central counterparty clearing

Within Central Counterparty Clearing, the Clearing House collects Initial Margin from its Clearing Members. The Initial Margin can be calculated in many ways, one of which is by applying the commonly used risk measure Value-at-Risk. However, Value-at-Risk has one major flaw, namely its inability to encapsulate Tail Risk. Due to this, there has for long been a desire to replace Value-at-Risk with Expected Shortfall, another risk measure that has shown to be much better suited to encapsulate Tail Risk. That said, Value-at-Risk is still used over Expected Shortfall, something which is mainly due to the fact that there is no consensus regarding how one should backtest Expected Shortfall. The goal of this thesis is to evaluate some of the most commonly proposed methods for backtesting Expected Shortfall. In doing this, several non-parametric backtests of Expected Shortfall are investigated using simulated data as well as market data from different types of securities. Moreover, this thesis aims to shed some light on the differences between Value-at-Risk and Expected Shortfall, highlighting why a change of risk measure is not as straightforward as one might believe. From the investigations of the thesis, several backtests are found to be sufficient for backtesting the Initial Margin with Expected Shortfall as the risk measure, the so called Minimally Biased Relative backtest showing the overall best performance of the looked at backtests. Further, the thesis visualizes how Value-at-Risk and Expected Shortfall are two risk measures that are inherently different in a real-world setting, emphasizing how one should be careful making conversions between the two based upon parametric assumptions