QF5202A
Structured Products
Homework Two
1. (a) Why the randomness in interest rate plays a secondary role in convertible bond price when compared with their non-convertible counterpart? Do convertible bond investors prefer negative correlation of interest rate and stock price? Explain your answer.
(b) Explain why the mandatory convertible securities should be structured with pro- vision of juicy coupons while the conversion premium is paid only when the stock price is performing. Name the key differences between investing the usual convertible bonds and mandatory convertible securities.
2. (a) Suppose the credit default swap premium s is below the par spread spar in the de-faultable par floater, how can an arbitrageur benefit from the attractive par spread? Show the arbitrage procedure in detail.
(b) Name two factors that may inhibit the full extraction of such arbitrage opportunities (specifying other potential risks embedded in these arbitrage transactions).
3. Consider the Guaranteed Minimum Withdrawal Benefit in Variable Annuities, explain why the Guarantee can be viewed as a zero-strike call option. Alternatively, the Guar- antee can be viewed as a put option with a random exercise time. What is the nature of this random time?
4. Suppose that the spot rate curve is flat at 6% with continuous compounding and a three-year defaultable bond with a coupon of 5% (paid semiannually) and par 100:00 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?
Hint: It is necessary to compute the time-0 value of the annuity stream paying $1 per annum (6 semi-annual payments during the 3-year life of the asset swap).
5. (a) The yield on a 5-year risk-free bond is 7%.
(b) The yield on a 5-year corporate bond issued by company X is 9:5%.
(c) A 5-year credit default swap providing insurance against the default of company X costs premium rate of 150 basis points per year.
What arbitrage opportunity is there in this situation? What arbitrage opportunity would there be if the credit default spread were 300 basis points instead of 150 basis points? Give two reasons why arbitrage opportunities such as those you identify may not be extracted fully by an arbitrageur.
6. A company enters into a total return swap where it receives the return on a corporate bond paying a coupon of 5% and pays LIBOR.
(a) Explain in details the differences between the total return swap and a regular interest rate swap, where 5% is exchanged for LIBOR.
(b) Both the total return swap and asset swap involve exchange of floatingrate payments for fixed rate paytments. What are their major differences?
7. Explain with two reasons why most synthetic CDO is partially funded where the total sum of principals of credit linked notes only represent a small fraction of the notional of the reference portfolio. Under high correlation of defaults, explain why it is more often to see high probability of fewer number of defaults and high probability of larger number of defaults. Explain why the senior tranche investors “short correlation”.