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...

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,...

State price densities (SPD) are an important element in applied quantitative finance. In a Black-Scholes model they are lognormal distributions with constant volatility parameter. In practice volatility changes and the distribution deviates from log-normality. We estimate SPDs using EUREX option...

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 paper concerns the fixed-width confidence intervals for location based on M- estimators in the location model. A robust three-stage procedure is proposed and its asymptotic properties are studied. The performance of the procedure depends on some tuning parameters. Their effect on the...

State price density (SPD) contains important information concerning market expectations. In existing literature, a constrained estimator of the SPD is found by nonlinear least squares in a suitable Sobolev space. We improve the behavior of this estimator by implementing a covariance structure...

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...

Establishing a standard formula (SF) for the regulation of European insurance companies is a Herculean task. It has to acknowledge very different business models and national peculiarities. In addition, regulatory authorities—as a stakeholder on their own—have a number of supervisory...

We present an analysis of VaR forecasts and P&L-series of all 13 German banks that used internal models for regulatory purposes in the year 2001. To this end, we introduce the notion of well-behaved forecast systems. Furthermore, we provide a series of statistical tools to perform our analyses....