The effect of the dependence structure on risk measures

After the financial crisis of 2008, the goodness of mathematical models became strongly questionable. One of the main targets of the attacks was the application of the Gaussian copula. The risk measures proposed were the Value at Risk (VaR) and Conditional Value at Risk (CVaR). We show how the values of these risk measures are influenced by different kinds of dependency structures, which are modelled by different copulas. Archimedean copulas are used for modelling tail dependences and asymmetrical dependencies. We present their impact on the portfolio’s probability distribution. We explain why in the case of multivariate distribution Gauss Copula andStudent copula are good alternatives. We also show how conditional independence can be used for giving more flexible approximations. We illustrate on simulated and also on real data the impact of the dependence structure on VaR and CVaR.