1. Consider the following problem:

The value of a companys equity is 4 million. The debt that will have to be repaid in two years is 15 million. The risk-free interest rate is 6% per annum. The value of the companys asset today is 17.084 million and volatility of assets (assumed constant) is 15.76%.

(i) Use Mertons model to estimate the expected loss from default, the probability of default, and the

recovery rate (as a percentage of the no-default value) in the event of default.

(ii) Explain why Mertons model gives a high recovery rate.

2. Suppose that a bank has a total of 150 million of retail exposures of varying sizes with each exposure being small in relation to the total exposure. The one-year probability of default for each loan is 2% and the loss given default for each loan is 35%. The copula correlation parameter is estimated as 0.3.

Calculate the 99.9% worst case default rate and the credit value-at-risk at a 99.9% confidence level using

Vasiceks model.