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On the Aggregation of Local Risk Models for Global Risk Management

Given a collection of single-market covariance matrix forecasts for different markets, we describe how to embed them into a global forecast of total risk. We do this by starting with any global covariance matrix forecast that contains information about cross-market correlations, and revising it to agree with the pre-specified submarket matrices, preserving the requirement that a covariance matrix be positive semi-definite. We characterize the ways this can be done and address the resulting numerical optimization problem.