1. Consider an A-rated bond and a B-rated bond. Assume that the one-year probabilities of default for the A- and B-rated bonds are 1% and 3%, respectively. Assume also that the factor sensitivities (to a single Gaussian common factor) of these bonds are 0.2 for the A-rated bond and 0.3 for the B-rated bond. Answer the following questions:
   1. What is the asset value correlation between the two bonds?
   2. What is the joint default probability of those bonds (within the Gaussian framework)?
   3. What is the default correlation of the two (within the Gaussian framework)?