a. Two borrowers, each with a default probability of 10%, have a joint default probability of 5%. What is the default correlation?

b. A portfolio contains 100 borrowers, each with a default probability of 1%. Assuming that defaults are independent, determine the probability of observing 1 default in the portfolio.

c. You are using an asset value model with an asset correlation of 6%. For one scenario of the Monte Carlo simulation, you draw the following random numbers: -2.0 for the factor, and -1.0 for the idiosyncratic shock of a borrower with a default probability of 5%. Does this borrower default in the scenario?