February 14th, 2003, 12:55 pm
Copula functions are particular functions linking other multivariate distributions. If we define n random variables:N1 N2 N3¡Nn we find a joint distribution function or copula D D(n1,n2¡,nn,sigma)=Pr [N1¡Ün1,N2¡Ün2¡,Nn¡Ünn] First build a multivariate function from given univariate functions Fi named a copula function Cop[f1(x1),f2(x2)¡Fn(xn)]=F(x1,x2,..xn)Risk managers use copulas to calculate joint default probability t for two or more correlated companies and related securities, once defined a default correlation parameter sigma, they try to calculate default correlation over specified and continous time intervals[0,t].When buying a CDSwap the buyer of protection the exact default risk correlation between seller (counterparty) and underlying reference asset of CDS; my doubts are referred to fitted choices of correlation sigma and their implications for pricing CDSW, thanks for any answer.