Before revision:  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,
After revision:  Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupling with default contagion could have the leading component of the total default risk as Das,