Value at risk calculation through ARCH factor methodology: Proposal and comparative analysis

In this paper we put forward a new method to estimate value at risk (VaR), autoregressive conditional heteroskedastic (ARCH) factor, which combines multivariate analysis with ARCH models. Firstly, from a set of correlated portfolio risk factors, we derive a smaller uncorrelated risk factors set, by applying multivariate analysis. Secondly, we use ARCH schemes to model uncorrelated factors historical behaviour. Thirdly, we use the estimated models to predict future values for factors standard deviation. From them, VaR calculation is immediate. In this way, ARCH factor methodology overcomes the multivariate ARCH models drawbacks, which, in practice, make these unworkable for VaR calculation purposes. We apply the proposed methodology over a set of foreign exchange risk exposed portfolios, obtaining better results than those reached when J.P. Morgan s Riskmetrics is used. 2003 Elsevier B.V. All rights reserved.