Before revision:  As an application, we employ the default contagion model to price synthetic CDOs. The calculation time is reduced dramatically comparing with related literatures, especially, when the number of reference obligors is large ]{ [ }  .
After revision:  Applying the new framework, we give analytical pricing formulaes for synthetic collateralized debt obligations (CDOs). The numerical studies validate our theory and its practical applications. Our empirical studies give the evidence that systematic default risk coupling with default contagion could have the leading component of the total default risk as Das, Duffie, Kapadia and Saita ]{ [ } .