Was Copula responsible for the financial crash of 2008?

First of all, let's understand the copula function and its rule.

Copula:

The term "copula" comes from Latin, meaning "join" or "link." Mathematically, a copula is a cumulative distribution function defined on [0,1]^2, where the margins follow a standard uniform distribution. For instance, if we have two random variables, X and Y, with a joint distribution function H(x,y) and marginal distributions F_x and G_y, then there exists a copula function C such that:

H(x,y) = C(F(x), G(y)).

A copula is a function that characterizes the relationship between random variables. Unlike traditional methods like the Pearson correlation coefficient (r), a copula captures the relationship's strength and shape. There are various copulas, each capable of modeling different dependencies between variables. For instance, Clayton's copula addresses lower tail dependency, while Gumbel and Joe's copulas focus on upper tail dependency. Consequently, a key challenge when using copula models is selecting the appropriate type; an incorrect choice can result in misleading and inaccurate outcomes.

Gaussian copula

The Gaussian (normal) copula is the most widely used copula function, but it has a crucial limitation: it cannot effectively address tail dependency.

Therefore, it is unjust to hold the Gaussian copula responsible for the 2008 financial crisis. Given this limitation, modelers must choose the most suitable copula function from various options (read, for example, Salmon 2009, Paul R. Dewick and Shuangzhe Liu 2022, and Fadhah Alanazi 2022).