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Figure 6.3: QQ Plot of S&P500 GARCH Shocks Against the Standardized t Distribution

Figure 6.3: QQ Plot of S&P500 GARCH Shocks Against the Standardized t Distribution

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The Asymmetric t distribution



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• If one would like to have skewness in t distribution, the asymmetric

t distribution can be used,



Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



The Asymmetric t distribution

• Here d1 > 2, and -1 < d2 < 1.

• Note that C(d1) = C(d) from the symmetric

Student’s t distribution



Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



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Figure 6.4: The Asymmetric t Distribution



Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



The Asymmetric t distribution

• In order to derive the moments of the distribution

we first define,



Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



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Figure 6.3: QQ Plot of S&P500 GARCH Shocks Against the Standardized t Distribution

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