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Elements of Financial Risk Management, 2nd Edition by Peter Christoffersen

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9. Distributions and Copulas for Integrated Risk Management
This chapter develops alternatives to the multivariate normal distribution. The multivariate normal distribution underestimates the joint probability of simultaneous large negative returns across assets. This in turn means that risk management models built on the multivariate normal distribution are likely to exaggerate the benefits of portfolio diversification. First, we define and plot threshold correlations, which will be our key graphical tool for detecting multivariate nonnormality. Second, we review the multivariate standard normal distribution, and introduce the multivariate standardized symmetric t distribution and the asymmetric extension. Third, we define and develop the copula ...

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