The relation between coherent risk measures, valuation bounds, and certain classes of portfolio optimization problems is established. One of the key results is that coherent risk measures are essentially equivalent to generalized arbitrage bounds, named "good deal bounds" by Cerny and Hodges (1999). The results are economically general in the sense that they work for any cash stream spaces, be it in dynamic trading settings, one-step models, or deterministic cash streams. They are also mathematically general as they work in (possibly infinitedimensional) linear spaces.The valuation theory presented seems to fill a gap between arbitrage valuation on the one hand and utility maximization (or equilibrium theory) on the other hand. "Coherent" valuation bounds strike a balance in that the bounds can be sharp enough to be useful in the practice of pricing and still be generic, i.e., somewhat independent of personal preferences, in the way many coherent risk measures are somewhat generic.

Abstract. Qualitative and quantitative properties of the Cornish-Fisher-Expansion in the context of Delta-Gamma-Normal approaches to the computation of Value at Risk are presented. Some qualitative deficiencies of the Cornish-Fisher-Expansion -the monotonicity of the distribution function as well as convergence are not guaranteed -make it seem unattractive. In many practical situations, however, its actual accuracy is more than sufficient and the Cornish-Fisher-approximation can be computed faster (and simpler) than other methods like numerical Fourier inversion. This paper tries to provide a balanced view on when and when not to use Cornish-Fisher in this context.

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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. The results shed light on the forecast quality of VaR models of the individual banks, the regulator's portfolio as a whole, and the main ingredients of the computation of the regulatory capital required by the Basel rules.

The present paper analyses the dependence structure between WTI and Brent crude oil spot log-returns using modern copula techniques. In a first step we apply several single equation models to the marginals to account for autocorrelation and volatility clustering. Second, to select both copulas and tail copulas characterising the joint dynamics between the time series we implement and evaluate newly introduced bootstrap-based goodness-of-fit tests. Based on each approach, a comprehensive backtesting is performed by simulating and comparing the risk measures Value-at-Risk and Expected Shortfall with historical values.