Backtesting Value-at-Risk Models: A Multivariate Approach
The purpose of this paper is to develop a new and simple backtesting procedure that ex- tends the previous work into the multivariate framework. We propose to use the multivariate Portmanteau statistic of Ljung-Box type to jointly test for the absence of autocorrelations and cross-correlations in the vector of hits sequences for di erent positions, business lines or nancial institutions. Simulation exercises illustrate that this shift to a multivariate hits dimension delivers a test that increases signi cantly the power of the traditional backtesting methods in capturing systemic risk: the building up of positive and signi cant hits cross-correlations which translates into simultaneous realization of large losses at several business lines or banks. Our multivariate procedure is addressing also an operational risk issue. The proposed technique provides a simple solution to the Value-at-Risk(VaR) estimates aggregation problem: the institution's global VaR measure being either smaller or larger than the sum of individual trading lines' VaRs leading to the institution either under- or over- risk exposure by maintaining excessively high or low capital levels. An application using Pro t and Loss and VaR data collected from two international major banks illustrates how our proposed testing approach performs in a realistic environment. Results from experiments we conducted using banks' data suggest that the proposed multivariate testing procedure is a more powerful tool in detecting systemic risk if it is combined with multivariate risk modeling i.e. if covariances are modeled in the VaR forecasts.
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- Delgado, Miguel A. & Carlos Escanciano, J., 2007. "Nonparametric tests for conditional symmetry in dynamic models," Journal of Econometrics, Elsevier, vol. 141(2), pages 652-682, December.
- Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
- Pérignon, Christophe & Smith, Daniel R., 2010. "Diversification and Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 55-66, January.
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