Dictionary > Finance > C > Copula Function

# Finance Dictionary - C Terms

# Copula Function

A copula function is simply a specification of how the univariate marginal distributions combine to form a multivariate distribution. For example, if we have N-correlated uniform random variables, U1, U2, . . . , UN, then C(u1,u2, . . . ,uN) ¼ Pr{U1 u1, U2 u2, . . . ,UN uN} is the joint distribution function that gives the probability that all of the uniforms are in the specified range. In a similar manner, we can define the Copula function for the default times of N assets C(F1(T1),F2(T2), . . . , FN(TN) ) ¼ Pr{U1 F1(T1),U2 F2(T2), . . . ,UN FN(TN)}, where Fi(Ti) ¼ Pr{ti t}. Li (2000) has shown that how copula function can be used to estimate default correlation. [See also Default correlation]