16.4 Recommended Literature

The classical start to Value at Risk (VaR) estimation lies in the consideration of linear or linearized portfolios, see RiskMetrics (1996). The linear structure transforms the multidimensional normally distributed random variables into one dimensional Gaussian values whose quantile can be estimated. An introduction to the asymptotic distributions of extreme values can be found in Leadbetter et al. (1983) and Embrechts et al. (1997). McAllister and Mingo (1996) describe the advantages from (15.13) in a RAROC (risk-adjusted return on capital) setup. Artzner et al. (1997) claim that the expected shortfall is a coherent measurement of risk. Jaschke and Küchler (1999) show that (15.13) is a reasonable approximation for a worst case scenario. Leadbetter et al. (1983) show how (15.13) can be used in the context of the theory of extreme values. A good overview of the VaR problems is given in Jorion (2000). The majority of the German laws can be found under www.bafin.de . Taleb (2001) is a critic of specific VaR definitions and gives several examples in which Value at Risk definitions can be ``blinding'' given certain trading strategies (``Peso Problem Traders''). A complete literture review can be found in Franke et al. (2000). There VaR calculations from Overbeck (2000) based on the ability to pay process are discussed and country risk is evaluated in Lehrbass (2000).