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correlation
Hi, if u have two credits with respective default probabilities p1 & p2, what's the expression for the correlationbetween the indicator functions of the two default events?thanks
correlation
hey, do you know the answer or not?
Last edited by epiccn on December 6th, 2004, 11:00 pm, edited 1 time in total.
correlation
This follows directly from the definition of basic statistical functions.Variance(X) = E(X^2) - E(X)E(X)Covariance(X,Y) = E(XY) - E(X)E(Y)Correlation(X,Y) = Covariance(X,Y)/[Variance(X)*Variance(Y)]^0.5For an indicator variable, E(X) = E(X^2) = p. E(XY) is just the joint probability of X and Y both being 1. So if p12 is the probability of joint default, the correlation coefficient is:(p12 - p1*p2)/[(p1 - p1^2)(p2 - p2^2)]^0.5= (p12 - p1*p2)/[p1*p2*(1-p1)*(1-p2)]^0.5