3 search hits
- 2008, 14
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Value-at-Risk and expected shortfall for rare events
(2008)
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Stefan Mittnik
Tina Yener
- We show that the use of correlations for modeling dependencies may lead to counterintuitive behavior of risk measures, such as Value-at-Risk (VaR) and Expected Short- fall (ES), when the risk of very rare events is assessed via Monte-Carlo techniques. The phenomenon is demonstrated for mixture models adapted from credit risk analysis as well as for common Poisson-shock models used in reliability theory. An obvious implication of this finding pertains to the analysis of operational risk. The alleged incentive suggested by the New Basel Capital Accord (Basel II), amely decreasing minimum capital requirements by allowing for less than perfect correlation, may not necessarily be attainable. JEL Classification : C52, G11, G32
- 2008, 08
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Multivariate regime–switching GARCH with an application to international stock markets
(2008)
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Markus Haas
Stefan Mittnik
- We develop a multivariate generalization of the Markov–switching GARCH model introduced by Haas, Mittnik, and Paolella (2004b) and derive its fourth–moment structure. An application to international stock markets illustrates the relevance of accounting for volatility regimes from both a statistical and economic perspective, including out–of–sample portfolio selection and computation of Value–at–Risk. JEL Classification: C32, C51, G10, G11
- 2008, 07
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Asymmetric multivariate normal mixture GARCH
(2008)
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Markus Haas
Stefan Mittnik
Marc S. Paolella
- An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is shown that the disaggregation of the conditional (co)variance process generated by the model provides substantial intuition. Moreover, the model exhibits a strong performance in calculating out–of–sample Value–at–Risk measures. JEL Classification: C32, C51, G10, G11
