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# 021 - 21 Swaps Economic Analysis and Pricing Answers to...

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214 Answers to Questions and Problems 1. A trader buys a bond that pays an annual coupon based on LIBOR with a principal amount of \$10 million. The actual payment in each year depends on the level of LIBOR observed one year previously. The same trader simultaneously sells a \$10 million dollar bond that pays a fixed rate of 7 percent interest and also has an annual coupon. Both bonds have a maturity of five years and are priced at par. The trader also enters a pay-fixed interest rate swap with annual payments, a tenor of five years, and a notional principal of \$10 mil- lion. For the swap, the fixed rate is 7 percent and the floating rate is LIBOR. The swap also pays in arrears. A. Construct a time line for each bond showing the payments associated with the bond. FRN Time Line: Coupon Bond Time Line: 0 1 2 3 4 5 Year \$10,000,000 \$700,000 \$700,000 \$700,000 \$700,000 \$700,000 + \$10,000,000 0 1 2 3 4 5 Year 0 LIBOR × \$10,000,000 1 LIBOR × \$10,000,000 2 LIBOR × \$10,000,000 3 LIBOR × \$10,000,000 4 LIBOR × \$10,000,000 \$10,000,000 + –\$10,000,000 21 Swaps: Economic Analysis and Pricing

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ANSWERS TO QUESTIONS AND PROBLEMS 215 B. Construct a time line showing the net payments resulting from the two bonds. Bond Portfolio Time Line: C. Construct a time line showing the payments for the swap. Pay-Fixed Swap Time Line: D. Based on the two time lines from parts B and C, what conclusion can you draw regarding the relationship between swaps and bond portfolios? A plain vanilla swap can be constructed or synthesized by a bond portfolio. This is the case, because the bond portfolio and the swap have identical cash flows. This suggests that the prices of bonds can be used to value swaps, and that swaps can be used to transform cash flow patterns on bond portfolios. 2. Assume that today is December 17, 2003. A firm enters a plain vanilla interest rate swap as the receive-fixed party on a swap with a tenor of one year, quarterly payments at the end of the next four quarters, and a notional principal of \$25 million. At the same time, this firm buys a strip of Eurodollar futures for the next four con- tracts, with 25 contracts per expiration. (Ignore daily settlement; in other words, assume that all futures-related cash flows occur at the expiration of the futures contract, which occurs at the end of each quarter.) At present, t 0, the LIBOR yield curve is flat at 8 percent, and the fixed rate on the swap is also 8 percent. A. Complete the following table using our familiar LIBOR t notation. Assume that the Eurodollar futures rate converges to LIBOR at expiration. 0 1 2 3 4 5 Year 0 LIBOR × \$10,000,000 1 LIBOR × \$10,000,000 2 LIBOR × \$10,000,000 3 LIBOR × \$10,000,000 4 LIBOR × \$10,000,000 \$700,000 \$700,000 \$700,000 \$700,000 \$700,000 0 1 2 3 4 5 Year 0 LIBOR × \$10,000,000 1 LIBOR × \$10,000,000 2 LIBOR × \$10,000,000 3 LIBOR × \$10,000,000 4 LIBOR × \$10,000,000 \$700,000 \$700,000 \$700,000 \$700,000 \$700,000 QuarterNet Receive-Fixed Swap Cash Flow Net Long Futures Cash Flow 0 0 0 1 (0.08 LIBOR 0 )/4 \$25,000,000 (0.08 LIBOR 1 )/4 \$25,000,000 2 (0.08 LIBOR 1 )/4 \$25,000,000 (0.08 LIBOR 2 )/4 \$25,000,000 3 (0.08 LIBOR 2 )/4 \$25,000,000 (0.08 LIBOR 3 )/4 \$25,000,000 4 (0.08 LIBOR 3 )/4 \$25,000,000 (0.08 LIBOR 4 )/4 \$25,000,000
216 CHAPTER 21 SWAPS : ECONOMIC ANALYSIS AND PRICING All of the futures contracts should be entered at 8 percent, because the yield curve is flat. The payoff on each futures depends on the deviation of spot LIBOR at expiration from the initial futures rate of 8 percent. With

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