Value at risk from the viewpoint of copulas

Abstract

The value at risk _VaR_, is a measure that quantifies the risks faced by a given portfolio. There are some methods to calculate the VaR: historical simulation, Montecarlo simulation, parametric models and duration and convexity models, among others. To calculate the VaR is required to model the portfolio returns and to find the loss distributions that describe them, traditionally those distributions are suppose to be normal distributed, but the empirical evidence shows the contrary. In the last few years, research in VaR calculation shows how copulas determine the dependence structure of a portfolio of the risky assets, without any assumptions regarding distributions, so you can find in it more realistic results and it is possible to avoid sub estimation of the value at risk of the portfolio.