Tail Dependence - ETH - Entrepreneurial Risks - ETH Zürich
Tail Dependence - ETH - Entrepreneurial Risks - ETH Zürich
Tail Dependence - ETH - Entrepreneurial Risks - ETH Zürich
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upper tail ˆσ upper tail ˆσ lower tail ˆσ lower tail ˆσ<br />
tail 1... k c... k 1... k c... k<br />
ˆχ<br />
BMY 0.94 0.09 0.92 0.09 0.50 0.05 0.94 0.09<br />
CVX 0.94 0.09 0.92 0.09 0.00* 0.00* 0.94 0.09<br />
HPQ 0.94 0.09 0.91 0.09 0.40 0.04 0.94 0.09<br />
KO 0.94 0.09 0.92 0.09 0.26 0.03 0.94 0.09<br />
MMM 0.94 0.09 0.92 0.09 0.42 0.04 0.94 0.09<br />
PG 0.94 0.09 0.92 0.09 0.46 0.05 0.94 0.09<br />
SGP 0.94 0.09 0.92 0.09 0.34 0.03 0.94 0.09<br />
TXN 0.94 0.09 0.92 0.09 0.52 0.05 0.94 0.09<br />
WAG 0.94 0.09 0.92 0.09 0.36 0.04 0.94 0.09<br />
Table 3.1: Estimated values of upper and lower tail dependence for S&P 500 index with a set<br />
of nine major assets traded on the New York stock Exchange calculated by a non-parametric<br />
approach: ˆχ +,− = Zk,N ·k<br />
� Zk,N 2 k(N−k)<br />
N and corresponding standard deviation: ˆσ (ˆχ) = N3 . The<br />
tail represents the most extreme 4% of the return values during a time interval from January<br />
1991 to December 2000. ’tail’ shows the calculation interval of L with c = 13 and k = 100,<br />
and ∗ denotes ˆχ �= 1 and therefore ˆχ = 0.<br />
upper tail ˆσ upper tail ˆσ lower tail ˆσ lower tail ˆσ<br />
tail 1... k c...k 1... k c... k<br />
ˆχ<br />
BMY 0.96 0.06 0.93 0.06 0.79 0.05 0.97 0.06<br />
CVX 0.96 0.06 0.93 0.06 0.35 0.02 0.97 0.06<br />
HPQ 0.96 0.06 0.92 0.06 0.74 0.05 0.97 0.06<br />
KO 0.93 0.06 0.93 0.06 0.54 0.04 0.97 0.06<br />
MMM 0.96 0.06 0.93 0.06 0.69 0.04 0.97 0.06<br />
PG 0.96 0.06 0.93 0.06 0.58 0.04 0.97 0.06<br />
SGP 0.96 0.06 0.93 0.06 0.74 0.05 0.97 0.06<br />
TXN 0.96 0.06 0.93 0.06 0.70 0.05 0.97 0.06<br />
WAG 0.96 0.06 0.93 0.06 0.73 0.05 0.97 0.06<br />
Table 3.2: Estimated values of upper and lower tail dependence for S&P 500 index with a set<br />
of nine major assets traded on the New York stock Exchange calculated by a non-parametric<br />
N and corresponding standard deviation: ˆσ (ˆχ) = N3 . The<br />
tail represents the most extreme 4% of the return values during a time interval from July<br />
1985 to April 2008. ’tail’ shows the calculation interval of L with c = 29 and k = 229, and ∗<br />
denotes ˆχ �= 1 and therefore ˆχ = 0.<br />
approach: ˆχ +,− = Zk,N ·k<br />
18<br />
� Zk,N 2 k(N−k)