Domestic Systemically Important Banks: A Quantitative Analysis for the Chinese Banking System

Table 3

Archimedean family of Copulas.

Copula	𝐶(𝑢,𝑣)	Generator 𝜑(𝑡)	Lower tail-dependence coefficient 𝜆^lo	Upper tail-dependence coefficient 𝜆^up
Gumbel Copula	exp−(−ln𝑢)^𝛼+(−ln𝑣)^𝛼1/𝛼	(−ln𝑡)^𝛼	0	2−2^−1/𝛼
Clayton Copula	(𝑢^−𝛼+𝑣^−𝛼)^−1/𝛼	𝑡^−𝛼−1	2^−1/𝛼	0
Frank Copula	−1𝛼𝑒ln1+^−𝑢𝛼−1𝑒^−𝑣𝛼−1𝑒^−𝛼−1	𝑒−ln^−𝑡𝛼−1𝑒^𝛼−1	0	0