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Figure 6.4: The Asymmetric t Distribution

Figure 6.4: The Asymmetric t Distribution

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The Asymmetric t distribution

• In order to derive the moments of the distribution

we first define,



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



42



The Asymmetric t distribution

The moments of the asymmetric t distribution can

be derived as



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



43



Figure 6.5: Skewness and Kurtosis in the

Asymmetric t Distribution



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



44



The Asymmetric t distribution

• Notice that the symmetric t distribution is nested in the

asymmetric t distribution and can be derived by setting

d1 = d, d2 = 0 which implies A = 0 and B = 1

• Therefore,



• which yields



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



45



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Figure 6.4: The Asymmetric t Distribution

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