Cópulas: uma alternativa para a estimação de modelos de risco multivariados

The biggest challenge in portfolio’s risk measures is to find the best way to aggregate risks. This aggregation should be done in the way where we can identify the diversification effect recognized in either asset position or portfólio. For instance, a lot of things has been done for create this definition, for example a Value at Risk (VaR) in the parametric approach uses of an assumption where all the risk factors follow the same marginal distribution, it will be a normal distribution. In this approach volatility and correlation matrix are the most important things for modeling correctly this dependence. In Historical Simulation approach, this method can be through of as estimating the distribution of the loss operator under the empirical distribution, so statistical estimation of the multivariate distribution is not necessary. In this case, the Copulas Theory provides a useful alternative because this approach allows us to create no multivariate distribution where no assumption is necessary for a neither marginal distribution or multivariate distribution. In this work, we are comparing this methodology with another risk measures approach for example: Multivariate parametric model’s VaR and an Expected Shortfall – Diagonal VEC, BEKK, EWMA, CCC, DCC – and Historical approach for VaR and ES. For this work we create a portfolio with identical position for all the factor and this factor will be: one year internal interest rate (Pré252), one year external interest rate (Cupom cambial 252), Bovespa Index, Dow Jones Index.