The assignment questions are to be completed in groups of two. Do not share your work with students from other groups. Only original work done by your group members is to be submitted. Plagiarism will not be tolerated in this class. The assignment will be marked based on (1) How you arrive at the solution, (2) Is the solution logical, consistent with the materials taught in class? (3) The presentation of your results. Remember, you must present your work in a clear and concise manner. How you communicate your work visually and verbally matters. You are require to submit a spreadsheet with your calculations for the numerical questions and a separate document with the answer for the conceptual questions and where you show the key steps involved to get the solution of the numerical questions.

Assignment due: April 10th by 11:59 pm (EST).

Question 1 (10 points)

The value of a company’s equity is $2.5 million and the volatility of the equity is 50%. The debt that will have to be paid in three years is $10 million. The risk-free interest rate is 2.5% per annum. 1. What is the difference between risk-neutral versus real-world probabilities?

  1. Use Merton’s model to estimate the probability of a default on the debt in the next three years.

Question 2 (20 points)

Suppose that you observe the following empirical distributions for stocks X and Y .

Value z P{X z} P{Y z}
0.1 8% 3%
0.2 18% 10%
0.3 40% 20%
0.4 50% 32%
0.5 65% 48%
0.6 78% 65%
0.7 90% 80%
0.8 95% 90%
0.9 98% 95%
  1. Plot the probability density functions (pdf) for both stocks. (5 pts)
  2. Compute (5 pts)
    • The hazard rates of stocks X and Y .
    • E{X} and E{Y }
  3. Assume that stocks X and Y have a correlation coefficient of 0. Use the gaussian copula to compute (10 pts)
    • P{X ≤ 0.6,Y ≤ 0.9}
    • P{X ≤ 0.8,0.3 ≤ Y ≤ 0.6}
    • E{X|Y = 0.7}
    • E{Y |X = 0.5}

Question 3 (10 points)

Consider following transactions with the same counterparty

  1. 3 year foreign exchange forward
    • Principal 900
    • Current Value -90
  2. 2 year option on stock
    • Principal 600
    • Current Value 55
  3. 7 year interest rate swap.
    • Principal 600
    • Current Value 90

Under Basel I, what is RWA WITH and WITHOUT netting if counterparty is a corporation? How much capital has to be set aside?

Question 4 (15 points)

Green Triangle company, a A-rated company, has a market credit spread of 140 basis points on a 7-year bond. The recovery rate is 40%. Calculate:

  1. The average hazard rate per year over 7 years using the data from table 19.1 at the end of thisassignment
  2. The average hazard rate per year over 7 years using credit spreads.
  3. What is the expected risk premium earned by bond traders
  4. What factors can help to explain the magnitude of the expected risk premium calculated inpart c.
  5. Assume next that the bond provides a coupon of 5% per year paid semi annually, has a yield of6% (with continuous compounding) and the risk free yield is flat at 3%(with continuous compounding). Assume that default occurs at the end of the year (right before coupon payments).

Estimate the default probability assuming that it is the same each year.

Question 5 (15 points)

Great Lakes Bank’s balance sheet (in billions USD) is shown below. Under Basel III requirements, bank management must ensure that the Net Stability Funding Ratio (NSFR) exceeds the minimum threshold.

Cash 5 Retail Deposits (Stable) 25
Treasury Bonds (>1 yr) 5 Retail Deposits (Less Stable) 15
Coporate Bonds rated A 5 Wholesale Deposits 40
Mortgages 15 Preferred Stock (>1 year) 5
Small Business Loans (<1 yr) 60 Tier 2 Capital 5
Fixed Assets 10 Tier 1 Capital 10
  1. What is the NSFR for Great Lakes Bank?
  2. If the ratio is below the threshold, consider the following two ideas to ensure that the NSFRthreshold for the bank is acceptable. (1) raise more stable retail deposits and keep proceeds in corporate bonds (AA & higher); (2) raise more wholesale deposits and put the proceeds into Gold. Do you have a preference of option 1 or 2?
  3. What would be the most efficient manner from an additional funding and investment point ofview to achieve the NSFR threshold.

Question 6 (15 points)

The assets of a bank consist of $200 million of loans to A-rated corporations with the principals being repayable at maturity. The Probability of Default for the corporation is estimated as 0.4% per year. The loan maturities are three years and the LGD is 45%.

  1. What is the total risk-weighted assets for credit risk under the Basel II advanced IRB approach?
  2. How much Tier 1 and Tier 2 capital is required?
  3. How does this compare with the capital required under the Basel II standardized approach andunder Basel I?
  4. How much equity capital (including that for the capital conservation buffer) will be requiredunder Basel III if the advanced IRB approach is used.

Question 7 (15 points)

  1. Explain the concept of wrong way risk and provide three examples of it.
  2. Explain the the relationship between bond yield, risk free rate, and CDS spreads
  3. Name 4 reasons that contributed to trigger the Global Financial Crisis (GFC).
  4. What are ABS CDO’s? what went wrong with them the during the GFC?
  5. Explain the concept of downgrade triggers and how it affected AIG durong the GFC.