Gaussian Copula Formula

AnnaBegins · November 23rd, 2006, 10:54 am

In the book "Credit Derivatives - the definitive guide" by Jon Gregory the formula to produce correlated random shocks is given as: Ri = (SQRT(rho))*Rm + (SQRT((1-rho))*EiIs this wrong? When I implement this the correlations don't match my targets... However, if i use the following formual they do match the targets: Ri = (rho)*Rm + (SQRT((1-rho^2))*EiShould i just throw the book in the bin? Cheers,

meteor · November 23rd, 2006, 4:34 pm

The two formula are correct: ie Ri has variance 1 in both cases, assuming Rm and Ei have variance 1. They only differ in term of the correlation parameter between Ri and Rj, in the first case:corr(Ri,Rj)=rhowhile in the secondcorr(Ri,Rj)=rho^2

AnnaBegins · December 4th, 2006, 12:39 pm

Thanks Meteor,However, when I implement this, the second version gives me correlations equal to rho....Could you show me the proof?

meteor · December 4th, 2006, 8:05 pm

here you go

AnnaBegins · December 5th, 2006, 8:30 am

Many thanks.