The Performance of Market Risk Models for Value at Risk and Expected Shortfall Backtesting : In the Light of the Fundamental Review of the Trading Book

Sammanfattning: The global financial crisis that took off in 2007 gave rise to several adjustments of the risk regulation for banks. An extensive adjustment, that is to be implemented in 2019, is the Fundamental Review of the Trading Book (FRTB). It proposes to use Expected Shortfall (ES) as risk measure instead of the currently used Value at Risk (VaR), as well as applying varying liquidity horizons based on the various risk levels of the assets involved. A major difficulty of implementing the FRTB lies within the backtesting of ES. Righi and Ceretta proposes a robust ES backtest based on Monte Carlo simulation. It is flexible since it does not assume any probability distribution and can be performed without waiting for an entire backtesting period. Implementing some commonly used VaR backtests as well as the ES backtest by Righi and Ceretta, yield a perception of which risk models that are the most accurate from both a VaR and an ES backtesting perspective. It can be concluded that a model that is satisfactory from a VaR backtesting perspective does not necessarily remain so from an ES backtesting perspective and vice versa. Overall, the models that are satisfactory from a VaR backtesting perspective turn out to be probably too conservative from an ES backtesting perspective. Considering the confidence levels proposed by the FRTB, from a VaR backtesting perspective, a risk measure model with a normal copula and a hybrid distribution with the generalized Pareto distribution in the tails and the empirical distribution in the center along with GARCH filtration is the most accurate one, as from an ES backtesting perspective a risk measure model with univariate Student’s t distribution with ⱱ ≈ 7 together with GARCH filtration is the most accurate one for implementation. Thus, when implementing the FRTB, the bank will need to compromise between obtaining a good VaR model, potentially resulting in conservative ES estimates, and obtaining a less satisfactory VaR model, possibly resulting in more accurate ES estimates. The thesis was performed at SAS Institute, an American IT company that develops software for risk management among others. Targeted customers are banks and other financial institutions. Investigating the FRTB acts a potential advantage for the company when approaching customers that are to implement the regulation framework in a near future.