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What are copulas?

In: Mathematical Finance [Edit categories]

Answer:

Answer

Copulas are an exremely useful tool used to build models of the joint behavior of multiple financial variables. They allow you to define a multivariate statistical distribution in two steps:

first you specify the marginal univariate distribution for each of the variables of interest
then you link the single univariate distributions via a copula in order to obtain a multivariate distribution

Basically, what the copula does is to specify the structure of the dependence among the variables, leaving their marginal distributions unaltered.

Mathematically, a copula is a scalar-valued function of n-variables. If you plug n univariate distribution functions into its n arguments you get a multivariate distribution function, which has the original n distribution functions as its marginals. Stated more formally (for the case of two variables), if C=C(u,v) is the copula and F(x) and G(y) are two univariate distribution functions, H=H(x,y)=C(F(x),G(y)) is a bivariate distribution function having C and G as its marginals.

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First answer by Pandoga. Last edit by Pandoga. Contributor trust: 158 [recommend contributor ]. Question popularity: 42 [recommend question].

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