Assessing temporal trends in Copula based value-at-risk using local estimation

Abstract

In this paper we use local estimation to assess temporal trends in copula based Value-at- Risk (VaR), despite the developed method be able to be applied to any risk measure based in the probability distribution of an asset portfolio. The estimation of any quantile-based risk measure, in particular the VaR, relies on the correct speci cation of the multivariate probability distribution of the assets composing the portfolio. Temporal changes in the portfolio volatility may follow from the autocorrelations in the squares of each margin, as well as from changes over time in the dependence structure among the components. In order to assess and model temporal trends in copula parameters, we used local likelihood methods. First it is carried on some Monte Carlo simulation experiments in order to illustrate the methodology, then we apply the methods for the VaR valuation of 10 portfolios composed of international stock indexes. Through the use of out-of-sample tests, we found that the local estimation outperforms the global estimation procedure.