Before revision:  The calculation time is reduced dramatically comparing with related literatures, especially, when the number of reference obligors is large ]{ [ }  .
After revision:  The calculation time is reduced dramatically comparing with related literatures, especially, when the number of reference obligors is large ]{ [ } demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .