Essays on Measuring Model Riskof Risk Measures

Abstract

The thesis contributes to the quantitative measurement of model risk of popular models for market risk measures (focusing on Value-at-Risk and Expected Shortfall, denoted by VaR and ES) and volatility forecasting in several ways, and it consists of three main chapters. The first main contribution is the introduction of measurement of the model risk of ES as the optimal correction needed to pass several ES backtests. We investigate the properties of our proposed measures of model risk from a regulatory perspective. The empirical results show that for the DJIA index, the smallest corrections are required for the ES estimates built using GARCH models. Furthermore, the 2.5% ES requires smaller corrections for model risk than the 1% VaR, which advocates the replacement of VaR with ES as recommended by the Basel Committee. Also, if the model risk of VaR is taken into account, then the corrections made to the ES estimates reduce by 50% on average. The second main contribution is the development of a new scoring functionbased model risk estimation methodology for measuring the joint model risk of the pair of risk measures, VaR and ES, at a given significance level. A simulation study is carried out to illustrate and analyze the proposed model risk measure across various market risk models. The newly proposed technique accounts for a large proportion of true model risk for a wide set of models popular in the risk management literature. An empirical analysis illustrates its application for different asset classes. The RiskMetrics model and Historical Simulation have the highest level of joint model risk and the highest ES model risk for various assets among all models considered. The third main contribution is the introduction of a new model risk estimation methodology for volatility models based on the QLIKE loss function. The reliability of the proposed measure has been verified via simulations and compared with the theoretical model risk measure. The efficiency of volatility models can be improved after adjusting variance estimates for model risk. In an empirical study based on several assets, among the models considered, the RiskMetrics method, RW1000 and the ARCH-type models are the most affected by model risk. We find that after crises, model risk increases for poorly fitting volatility models.