Die Berechnung des VaR führt zur Reduktion der Dimension des Raumes der Risikofaktoren. Die vorzunehmenden Vereinfachungen resultieren aus unterschiedlichen Beweggründen, z.B. technische Effizienz, Sachlogik der Ergebnisse und statistische Adäquanz des Modells. Im Kapitel 2 stellen wir drei...

VaR models are related to statistical forecast systems. Within that framework different forecast tasks including Value-at-Risk and shortfall are discussed and motivated. A backtesting method based on the shortfall is developed and applied to VaR forecasts of areal portfolio. The analysis shows...

The Value-at-Risk calculation reduces the dimensionality of the risk factor space. The main reasons for such simplifications are, e.g., technical efficiency, the logic and statistical appropriateness of the model. In Chapter 2 we present three simple mappings: the mapping on the market index,...

The paper describes our experience with the production of electronic textbooks. Electronic books are defined as supplements to usual printed textbooks. The first part of the paper describes the technical background of our electronic book system. In the second part we describe how this system can...

The state price density is a second derivative of the discounted European options prices with respect to the strike price. We use Maximum Likelihood method to derive a simple estimator of the curve such that it is decreasing, convex and its second derivative integrates to one. Confidence...

We develop a procedure for monitoring changes in the error distribution of autoregressive time series while controlling the overall size of the sequential test. The proposed procedure, unlike standard procedures which are also referred to, utilizes the empirical characteristic function of...

We present an analysis of the VaR forecasts and the P&L series of all 12 German banks that used internal models for regulatory purposes throughout the period from the beginning of 2001 to the end of 2004. One task of a supervisor is to estimate the 'recalibration factor', i.e. by how much a bank...

Model risk as part of the operational risk is a serious problem for financial institutions. As the pricing of derivatives as well as the computation of the market or credit risk of an institution depend on statistical models the application of a wrong model can lead to a serious over- or...