FINA 556 – Structured Products and Exotic Options Homework One Spring 2010 Course instructor: Prof. Y.K. Kwok 1. A company that is uncertain about the exact date when it will pay or receive a foreign currency may try to negotiate with its bank a forward contract that specifies a period during which delivery can be made. The company wants to reserve the right to choose the exact delivery date to fit in with its own cash flows. Put yourself in the position of the bank. How would you price the product that the company wants? Think about a product that is similar to the “Flexible Notional Currency Forward”. 2. Consider a Treasury bond with a face value of $10,000, a coupon of 8% and several years to maturity. Currently this bond is selling for $9,260, and the previous coupon has just been paid. What is the forward price for delivery of this bond in 1 year? Assume that interest rates for 1 year out are flat at 9%. 3. The Z corporation issues a 10%, 20-year bond at a time when yields are 10%. The bond has a call provision that allows the corporation to force a bondholder to redeem his or her bond at face value plus 5%. After 5 years the corporation finds that exercise of this call provision is advantageous. What can you deduce about the yield at that time? (Assume one coupon payment per year). Hint: Find the yield such that the present value of the future coupons (from 6th to 20th year) plus the par at maturity equal to the call price offered by the issuer upon call. The yield of the bond must be lower than the yield computed above since the market price of the bond should be above the call price to induce the call. 4. Use the SEMBCORP INDUSTRIES LTD accumulator as an example (see lecture note), show how to decompose the product into a portfolio of forward contracts and put options with knock-out feature. Think about the hedging strategy also. Practitioners tend to think of an accumulator as a portfolio of usual knock-out options. Explain the deficiencies in this form of decomposition. 5. Suppose that the LIBOR curve is flat at 6% with continuous compounding and a three- 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? 6. Let C′(0) denote the time-0 price of the default-free fixed coupon bond paying coupon c − sA(0). Let s denote the par swap rate and A(0) denote the value of annuity stream (defined in the lecture note). Relate sA(0) with s, c and C′(0). 7. 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. Explain the difference between this and a regular swap where 5% is exchanged for LIBOR. 8. What are the potential risks faced by the total return payer? Also, explain some of the major differences between a total return swap and an asset swap. 1 9. Company X is based in the United Kingdom and would like to borrow $50 million at a fixed rate of interest for 5 years in US funds. Since the company is not well known in the United Kingdom, this has proved to be impossible. However, the company has been quoted 12% per annum on fixed-rate five-year sterling funds. Company Y is based in the United States and would like to borrow the equivalent of $50 million in sterling for 5 years at a fixed rate of interest. It has been unable to get a quote but has been offered US dollars at 10.5% per annum. Five-year government bonds currently yield 9.5% per annum in the United States and 10.5% in the United Kingdom. Suggest an appropriate currency swap that will net the financial intermediary 0.5% per annum. 10. Consider the currency swap structured between IBM and World Bank as discussed in the lecture note. Recalling one of the rationales for entering into these transactions is that IBM would like to capture the favorable exchange rate of US dollar over DM and Swiss Franc at that time. Explain how (i) IBM can capture the favorable exchange rate by the currency swap; (ii) World Bank realizes the favorable exchange rate by entering into the US dollar bond market. 11. “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. 12. Show that the value of a coupon-bearing corporate bond is the sum of the values of its constituent zero-coupon bonds when the claim amount 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. 13. An investor purchases a 10-year AA corporate bond that is puttable to the issuer at year 5. The puttable bond yields 7.00% pa (versus the comparable yield on conventional ten year non-puttable 10-year AA corporate bond of 7.5% pa). How to monetize the puttable right using a swaption? Describe the nature of payoff of the swaption. What would be the option premium charged on the swaption per annum in order that it is more advantageous for the investor to own the puttable bond (which has a lower yield than that of its non-puttable counterpart)? 14. Assume that the following market conditions exist: • 5-year AA corporate bonds with a one time call at the end of third year are trading at 8.3% pa • 5-year AA corporate non-callable bonds are trading at 7.50% pa • Receiver swaption at 7.50% pa is priced at a 180bps premium, where the dealer can require the investor to pay 7.5% pa and receive US$ LIBOR for Year 4 and Year 5 • 5-year AA non-callable floating rate bond yielding US$LIBOR • 3-year and 5-year fixed-floating interest rate swaps, where the floating rate is US$LIBOR Assume that an investor wishes to create a “synthetic” callable bond (same as the first bond listed above) using a non-callable bond (either fixed rate or floating rate) and swaps and / or swaption. Discuss various strategies that can be adopted using the instruments listed above. Describe the cash flows under different scenarios. Is it more advantageous to own the “synthetic” callable bond (make your own assumptions about the swap rates in the interest rate swaps)? 2 15. A differential swap may involve three currency worlds: interest payments are calculated based on the floating LIBOR of two currencies but the actual payments are denominated in a third currency. Show that this type of 3-currency differential swap can be decomposed into a portfolio of standard type of differential swaps which involve only two currency worlds. 16. A credit default swap requires a premium of 60 basis points per year paid semiannually. The principal is $300 million and the credit default swap is settled in cash. A default occurs after 4 years and two months, and the calculation agent estimates that the price of the reference bond is 40% of its face value shortly after the default. List the cash flows and their timing for the seller of the credit default swap. 17. Suppose that the risk-free zero curve is flat at 6% per annum with continuous compound- ing and that defaults can occur at times 1 years, 2 years, 3 years and 4 years in a four-year plain vanilla credit default swap with semiannual payments. Suppose that the recovery rate is 20% and the probabilities of default at times 1 year, 2 years, 3 years and 4 years are 0.01, 0.015, 0.02 and 0.025, respectively. The reference obligation is a bond paying a coupon semiannually of 8% per year. Defaults always take place immediately before coupon-payment dates on this bond. What is the credit default swap spread? What would the credit default spread be if the instrument were a binary credit default swap? 18. Suppose that the five-year risk-free yield is 4% and the five-year yield on bonds issued by corporation is 5.6% both with semiannual compounding. Estimate the CDS spread when the corporation is the reference entity, the reference liability is an 8% coupon bond, and the expected recovery rate is 40%. Assume that semiannual payments on the CDS. 19. Prove that a binary swap spread when the expected recovery rate is 50% is typically about 80% higher than when the expected recovery rate is 10% (Hint: Assume that the payoff from a regular credit default swap is the payoff from a binary credit default swap times one minus the recovery rate.) 20. Suppose that: (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 company X defaulting costs 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 are less than perfect.