What is a copula and why use one?

hard

Answer

$F(x, \;y)\; = \;C(F_{X}(x), \;F_{Y}(y))$
$Sklar's theorem: unique C for continuous margins.$
$Uses: multivariate density estimation when marginals are heavy-tailed but dependence is simpler (finance risk, joint failure modeling).$
$Gaussian copula, t-copula, Archimedean copulas (Clayton, Gumbel) — different tail dependence structures.$
$Foundational in quantitative finance.$

Check yourself — multiple choice

Random
$F(x, \;y)\; = \;C(F_{X}(x), \;F_{Y}(y))$ ; separates margins from dependence via Sklar's theorem; Gaussian / t / Archimedean copulas; standard in finance risk modeling
Same as GMM
Not real

Copula: separate marginals from dependence via Sklar's theorem; finance.

#density

214 interview questions in this topic.