The other critical assumption in the rating models relates to the default correlation of securitized assets. Suppose that a bank holds two loans, each with a default probability of pD and paying $0 on default and $100 otherwise. If the bank securitizes the two loans and transfers them to a SPE that issues two ABS tranches, the junior tranche bears the first $100
of losses, while the senior tranche bears losses only when the capital of the junior tranche is exhausted. Therefore, in order to compute the expected cash flows of the senior tranche, it is necessary to compute the joint probability of default.For instance, if each of the two loans has a 10 percent default probability and defaults are uncorrelated, the senior tranche will have only a 1 percent chance of default, but if the defaults of the two loans are perfectly correlated, both either survive or default simultaneously, so the securitization transaction would not decrease the default probability of the senior tranche. The absence of correlation among the subprime loans’ default probabilities relied on the direction of house prices and debt
market liquidity. When house prices firmly appreciate and the debt market is sufficiently liquid, a subprime mortgagor finds cash-out refinancing easy to obtain. Under those circumstances, the default reflects specific circumstances that prevent the mortgagor from obtaining cash-out refinancing, despite its general availability. Therefore, the default of a mortgagor has minimal implications on other subprime mortgages.