Tail Dependence - ETH - Entrepreneurial Risks - ETH Zürich

4.4 Assets included in indexes ’MERVAL’, ’MIBTEL’, ’NASDAQ’, and ’SMI’
that were used for the implementation of the different concepts given by
their name, further used abbreviation, and country of origin. . . . . . . 133
4.5 Assets included in indexes ’S&P 500’, ’SSEC’, and ’TA 100’ that were
used for the implementation of the different concepts given by their name,
further used abbreviation, and country of origin. Additional assets included
in index S&P 500 that were not part of the reference samples
presented in chapter (3) are listed below ’new assets’. . . . . . . . . . . 134
4.6 Estimated upper and lower tail dependence ˆ λ +,− applying the non-parametric
and parametric approaches according to Sornette & Malevergne to index
S&P 500 and 16 assets included in dependence of their component
weights in the index denoted by ’C.W.’ and β. The data samples contain
N = 2000 daily price observations on a range from 12.04.2000 to
31.03.2008. Tail index ˆν was calculated using Hill’s estimator, k =
0.04 · N = 80, c = 0.005 · N = 10, and ∗ denotes negative ˆ β. . . . . . . 135
4.7 Estimated upper and lower tail dependence ˆ λ +,− applying the non-parametric
approach according to Sornette & Malevergne to index S&P 500 and 16
assets included using βSI only calculated for the extreme tails by first
and second β-smile conditions. Component weights of assets within the
index are denoted by ’C.W.’, βSI for the first and second conditions and
β calculated for all data are listed to observe their impact on the estimates.
The data samples contain N = 2000 daily price observations on a
time interval from 12.04.2000 to 31.03.2008. Tail index ˆν was calculated
using Hill’s estimator. ’Cond 1’ denotes: Y ≥ Y (k) ∩ X ≥ X(k), ’Cond.
2’ denotes Y ≥ Y (k), k = 0.04 · N = 80, c = 0.005 · N = 10, and ∗
denotes negative ˆ β. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.8 Estimated upper and lower tail dependence ˆ λ +,− applying the parametric
and the non-parametric approach according to Sornette & Malevergne
to index Dow Jones Industrial Average and 12 assets included using β
calculated by all data. Component weights of assets within the index
are denoted by ’C.W.’, and β calculated for all data are listed to observe
their impact on the estimates. The data samples contain N = 2000 daily
price observations on a time interval from 16.08.2000 to 31.07.2008. Tail
index ˆν was calculated using Hill’s estimator, k = 0.04 · N = 80, and
c = 0.005 · N = 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.9 Estimated upper and lower tail dependence ˆ λ +,− applying the non-parametric
approach according to Sornette & Malevergne to index Dow Jones Industrial
Average and 12 assets included using βSI only calculated for
the extreme tails by first and second β-smile conditions. Component
weights of assets within the index denoted by ’C.W.’, βSI for the first
and second conditions and β calculated for all data are listed to observe
their impact on the estimates. The data samples contain N = 2000 daily
price observations on a time interval from 16.08.2000 to 31.07.2008. Tail
index ˆν was calculated using Hill’s estimator, k = 0.04 · N = 80, and
c = 0.005 · N = 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138