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...

This paper derives conditions for the existence of fourth moments of multivariate GARCH processes in the general vector specification and gives explicit results for the fourth moments and autocovariances of the squares and cross-products. Results are provided for the kurtosis and co-kurtosis...

We provide a framework for the analysis of term structures of credit spreads on corporate bonds in the presence of informational asymmetries. While bond investors observe default incidents, we suppose that they have incomplete information on the firm's assets and/or the threshold asset level at...

We propose a model of correlated multi-firm default with incomplete information. While public bond investors observe issuers' assets and defaults, we suppose that they are not informed about the threshold asset level at which a firm is liquidated. Bond investors form instead a prior on these...

The market for derivatives with payoffs contingent on the credit quality of a number of reference entities has grown considerably over recent years. The risk analysis and valuation of such multi-name structures often relies on simulating the performance of the underlying credits. In this paper...

Credit risk refers to the risk of incurring losses due to unexpected changes in the credit quality of a counterparty or issuer. In this paper we give an introduction to the modeling of credit risks and the valuation of credit-risky securities. We consider individual as well as correlated credit...

In a complete financial market every contingent claim can be hedged perfectly. In an incomplete market it is possible to stay on the safe side by superhedging. But such strategies may require a large amount of initial capital. Here we study the question what an investor can do who is unwilling...

An investor faced with a contingent claim may eliminate risk by (super-)hedging in a financial market. As this is often quite expensive, we study partial hedges, which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal...