An efficient method for market risk management under multivariate extreme value theory approach Miloˇ s Boˇ zovi´ c * Department of Economics and Business Universitat Pompeu Fabra, Barcelona February 22, 2009 Abstract This paper develops an efficient multivariate extreme-value approach to calcu- lating Value at Risk (VaR) and expected shortfall. It is based on the notion that some key results of the univariate extreme value theory can be applied sep- arately to a set of orthogonal random variables, provided they are independent and identically distributed. Such random variables can be constructed from the principal components of ARMA-GARCH conditional residuals of a multivari- ate return series. The model’s forecasting ability is then tested on a portfolio of foreign currencies. The results indicate that the generalized Pareto distri- bution of peeks over treshold of residuals performs well in capturing extreme events. In particular, model backtesting shows that the proposed multivariate approach yields more precise VaR forecasts than the usual methods based on conditional normality, conditional t-distribution or historical simulation, while maintaining the efficiency of conventional multivariate methods. * Email address: milos.bozovic@upf.edu