Frank
Gujarat shows that in 3.24. But truly, this is a little formula that most will just want to commit to memory (and neglect, “how the sausage is made”). I’d focus instead on being able to deploy it; e.g.,
1. if you know it, then you know variance (X) = cov(x,x) = E(X^2) - E(X)^2
2. In credit, we see EL = (PD)(LGD). we can use above to see: E(PD*LGD) = E(PD)E(LGD) + COV(PD,LGD). Since Ong et al in credit, and Basel 2, are using E(PD*LGD) = E(PD)E(LGD), then they must be assuming independence btwn PD & LGD.
David
