Verify (a) that the numbers in the second column of Table 24.3 are consistent with the

The spread between the yield on a 3-year corporate bond and the yield on a similar riskfree bond is 50 basis points. The recovery rate is 30%. Estimate the average hazard rate per year over the 3-year period.

Suppose that in Problem 24.1 the spread between the yield on a 5-year bond issued by the same company and the yield on a similar risk-free bond is 60 basis points. Assume the same recovery rate of 30%. Estimate the average hazard rate per year over the 5-year period. What do your results indicate about the average hazard rate in years 4 and 5?

Should researchers use real-world or risk-neutral default probabilities for (a) calculating credit value at risk and (b) adjusting the price of a derivative for defaults?

How are recovery rates usually defined?

Explain the difference between an unconditional default probability density and a hazard rate.

Verify (a) that the numbers in the second column of Table 24.3 are consistent with the numbers in Table 24.1 and (b) that the numbers in the fourth column of Table 24.4 are consistent with the numbers in Table 24.3 and a recovery rate of 40%.

Describe how netting works. A bank already has one transaction with a counterparty on its books. Explain why a new transaction by a bank with a counterparty can have the effect of increasing or reducing the banks credit exposure to the counterparty.

DVA can improve the bottom line when a bank is experiencing financial difficulties. Explain why this statement is true.

Explain the difference between the Gaussian copula model for the time to default and CreditMetrics as far as the following are concerned: (a) the definition of a credit loss and (b) the way in which default correlation is modeled.

Suppose that the LIBOR/swap curve is flat at 6% with continuous compounding and a 5-year bond with a coupon of 5% (paid semiannually) sells for 90.00. How would an asset swap on the bond be structured? What is the asset swap spread that would be calculated in this situation?

Show that the value of a coupon-bearing corporate bond is the sum of the values of its constituent zero-coupon bonds when the amount claimed in the event of default is the no-default value of the bond, but that this is not so when the claim amount is the face value of the bond plus accrued interest.

A 4-year corporate bond provides a coupon of 4% per year payable semiannually and has a yield of 5% expressed with continuous compounding. The risk-free yield curve is flat at 3% with continuous compounding. Assume that defaults can take place at the end of each year (immediately before a coupon or principal payment) and that the recovery rate is 30%. Estimate the risk-neutral default probability on the assumption that it is the same each year.

A company has issued 3- and 5-year bonds with a coupon of 4% per annum payable annually. The yields on the bonds (expressed with continuous compounding) are 4.5% and 4.75%, respectively. Risk-free rates are 3.5% with continuous compounding for all maturities. The recovery rate is 40%. Defaults can take place halfway through each year. The risk-neutral default rates per year are Q1 for years 1 to 3 and Q2 for years 4 and 5. Estimate Q1 and Q2.

Suppose that a financial institution has entered into a swap dependent on the sterling interest rate with counterparty X and an exactly offsetting swap with counterparty Y. Which of the following statements are true and which are false? (a) The total present value of the cost of defaults is the sum of the present value of the cost of defaults on the contract with X plus the present value of the cost of defaults on the contract with Y. (b) The expected exposure in 1 year on both contracts is the sum of the expected exposure on the contract with X and the expected exposure on the contract with Y. (c) The 95% upper confidence limit for the exposure in 1 year on both contracts is the sum of the 95% upper confidence limit for the exposure in 1 year on the contract with X and the 95% upper confidence limit for the exposure in 1 year on the contract with Y. Explain your answers.

A long forward contract subject to credit risk is a combination of a short position in a no-default put and a long position in a call subject to credit risk. Explain this statement.

Explain why the credit exposure on a matched pair of forward contracts resembles a straddle.

Explain why the impact of credit risk on a matched pair of interest rate swaps tends to be less than that on a matched pair of currency swaps.

When a bank is negotiating currency swaps, it should try to ensure that it is receiving the lower interest rate currency from a company with a low credit risk. Explain why.

Does putcall parity hold when there is default risk? Explain your answer.

Suppose that in an asset swap B is the market price of the bond per dollar of principal, B is the default-free value of the bond per dollar of principal, and V is the present value of the asset swap spread per dollar of principal. Show that V B B.

Show that under Mertons model in Section 24.6 the credit spread on a T-year zerocoupon bond is lnNd2 Nd1=L=T, where L DerT =V0.

Suppose that the spread between the yield on a 3-year zero-coupon riskless bond and a 3-year zero-coupon bond issued by a corporation is 1%. By how much does Black ScholesMerton overstate the value of a 3-year European option sold by the corporation.

Give an example of (a) right-way risk and (b) wrong-way risk.

Suppose a 3-year corporate bond provides a coupon of 7% per year payable semiannually and has a yield of 5% (expressed with semiannual compounding). The yields for all maturities on risk-free bonds is 4% per annum (expressed with semiannual compounding). Assume that defaults can take place every 6 months (immediately before a coupon payment) and the recovery rate is 45%. Estimate the hazard rate (assumed constant) for the three years.

A company has 1- and 2-year bonds outstanding, each providing a coupon of 8% per year payable annually. The yields on the bonds (expressed with continuous compounding) are 6.0% and 6.6%, respectively. Risk-free rates are 4.5% for all maturities. The recovery rate is 35%. Defaults can take place halfway through each year. Estimate the risk-neutral default rate each year.

Explain carefully the distinction between real-world and risk-neutral default probabilities. Which is higher? A bank enters into a credit derivative where it agrees to pay $100 at the end of 1 year if a certain companys credit rating falls from A to Baa or lower during the year. The 1-year risk-free rate is 5%. Using Table 24.5, estimate a value for the derivative. What assumptions are you making? Do they tend to overstate or understate the value of the derivative

The value of a companys equity is $4 million and the volatility of its equity is 60%. The debt that will have to be repaid in 2 years is $15 million. The risk-free interest rate is 6% per annum. Use Mertons model to estimate the expected loss from default, the probability of default, and the recovery rate in the event of default. (Hint: The Solver function in Excel can be used for this question, as indicated in footnote 10.)

Suppose that a bank has a total of $10 million of exposures of a certain type. The 1-year probability of default averages 1% and the recovery rate averages 40%. The copula correlation parameter is 0.2. Estimate the 99.5% 1-year credit VaR.

Extend Example 24.5 to calculate CVA when default can happen in the middle of each month. Assume that the default probability per month during the first year is 0.001667 and the default probability per month during the second year is 0.0025.

Calculate DVA in Example 24.5. Assume that default can happen in the middle of each month. The default probability of the bank is 0.001 per month for the two years.