1. Consider the following problem: The value of a company’s equity is £4 million. The debt that will have to be repaid i

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1. Consider the following problem:
The value of a company’s 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
company’s asset today is £17.084 million and volatility of assets
(assumed constant) is 15.76%.
(i) Use Merton’s 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 Merton’s 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
Vasicek’s model.