Validierung von Konzepten zur Messung des Marktrisikos: Insbesondere des Value at Risk und des Expected Shortfall - Fabian Mehmke; Heinz Cremers; Natalie Packham (Frankfurt School of Finance & Management, 2012)
– Market risk management is one of the key factors to success in managing financial institutions. Underestimated risk can have desastrous consequences for individual companies and even whole economies, not least as could be seen during the recent crises. Overestimated risk, on the other side, may have negative effects on a company's capital requirements. Companies as well as national authorities thus have a strong interest in developing market risk models that correctly quantify certain key figures such as Value at Risk or Expected Shortfall. This paper presents several state of the art methods to evaluate the adequacy of almost any given market risk model. Existing models are enhanced by in-depth analysis and simulations of statistical properties revealing some previously unknown effects, most notably inconsistent behaviour of alpha and beta errors. Furthermore, some new market risk validation models are introduced. In the end, a simulation with various market patterns demonstrates strenghts and weaknesses of each of the models presented under realistic conditions.
Keywords: C01; C02; C12; C13; C14; C15; C32; G32; G38; 330; Backtesting; Market Risk; Value at Risk; Expected Shortfall; Validation; Alpha Error; Beta Error; Time Until First Failure; Proportion of Failure; Traffic Light Approach; Magnitude of Loss Function; Markow-Test; Gauss-Test; Rosenblatt; Kuiper; Kolmogorov-Smirnov; Jarque-Bera; Regression; Likelihood Ratio; Truncated Distribution; Censored Distribution; Simulation