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Expected loss (EL) on credit asset if PD, LGD are correlated

Expected loss (EL) calculations typically assume no correlation (i.e., they assume independence) between probability of default (PD) and loss given default (LGD). Basel II internal ratings-based (IRB) approach to a capital charge assumes independence between PD & LGD. How can we compute expected loss (EL) if there is correlation between EDF/PD and LGD/recovery?
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