Figure 9.6: Simulated Threshold Correlations from the Bivariate Normal Copula with Various Copula Correlations
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t Copula
• t Copula is copula model built from the t distribution
• Consider first the bivariate case.
• The bivariate t copula CDF is defined by
• where
denotes the symmetric multivariate t
distribution
•
denotes the inverse CDF of the symmetric
univariate t distribution
Elements of Financial Risk Management Second Edition â 2012 by Peter Christoffersen
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t Copula
The corresponding bivariate t copula PDF is
Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen
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Figure 9.7: Simulated Threshold Correlations from the
Symmetric t Copula with Various Parameters
Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen
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t Copula
• The t copula can generate large threshold correlations
for extreme moves in the assets
• Furthermore it allows for individual modeling of the
marginal distributions, which allows for much
flexibility in the resulting multivariate distribution
Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen
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