Asymptotic Value-at-Risk Estimates for Sums of Dependent Random Variables

Mario V. Wüthrich

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Probability and Risk Models Financial Risk and Volatility Modeling Risk and Portfolio Optimization

Abstract

We estimate Value-at-Risk for sums of dependent random variables. We model multivariate dependent random variables using archimedean copulas. This structure allows one to calculate the asymptotic behaviour of extremal events. An important application of such results are Value-at-Risk estimates for sums of dependent random variables.

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1999An Introduction to Copulas 1994Modelling of extremal events in insurance and finance 2002Correlation and Dependence in Risk Management: Properties and Pitfalls 1998Understanding Relationships Using Copulas 1999Fitting bivariate loss distributions with copulas 2002Copula convergence theorems for tail events 2001Modelling dependent defaults 1998Modeling and Comparing Dependencies in Multivariate Risk Portfolios

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