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Unformatted text preview: Chapter 7 Interest Rate Forwards and Futures Question 7.1. Using the bond valuation formulas (7.1), (7.3), (7.6) we obtain the following yields and prices: Maturity ZeroCoupon Bond Zero Coupon OneYear Par Cont. Comp. Zero Yield Bond Price Implied Forward Coupon Yield Rate 1 0.04000 0.96154 0.04000 0.04000 0.03922 2 0.04500 0.91573 0.05003 0.04489 0.04402 3 0.04500 0.87630 0.04500 0.04492 0.04402 4 0.05000 0.82270 0.06515 0.04958 0.04879 5 0.05200 0.77611 0.06003 0.05144 0.05069 Question 7.2. The coupon bond pays a coupon of $60 each year plus the principal of $1,000 after ve years. We have cash ows of [ 60 , 60 , 60 , 60 , 1060 ] . To obtain the price of the coupon bond, we multiply each cash ow by the zerocoupon bond price of that year. This yields a bond price of $1,037.25280. Question 7.3. Maturity ZeroCoupon Zero Coupon OneYear Par Coupon Cont. Comp. Zero Bond Yield Bond Price Implied Forward Yield Rate 1 0.03000 0.97087 0.03000 0.03000 0.02956 2 0.03500 0.93351 0.04002 0.03491 0.03440 3 0.04000 0.88900 0.05007 0.03974 0.03922 4 0.04500 0.83856 0.06014 0.04445 0.04402 5 0.05000 0.78353 0.07024 0.04903 0.04879 89 Part 2 Forwards, Futures, and Swaps Question 7.4. Maturity ZeroCoupon Zero Coupon OneYear Par Coupon Cont. Comp. Zero Bond Yield Bond Price Implied Forward Yield Rate 1 0.05000 0.95238 0.05000 0.05000 0.04879 2 0.04200 0.92101 0.03406 0.04216 0.04114 3 0.04000 0.88900 0.03601 0.04018 0.03922 4 0.03600 0.86808 0.02409 0.03634 0.03537 5 0.02900 0.86681 0.00147 0.02962 0.02859 Question 7.5. Maturity ZeroCoupon Zero Coupon OneYear Par Coupon Cont. Comp. Zero Bond Yield Bond Price Implied Forward Yield Rate 1 0.07000 0.93458 0.07000 0.07000 0.06766 2 0.06000 0.88999 0.05009 0.06029 0.05827 3 0.05000 0.86384 0.03028 0.05065 0.04879 4 0.04500 0.83855 0.03016 0.04578 0.04402 5 0.04000 0.82193 0.02022 0.04095 0.03922 Question 7.6. In order to be able to solve this problem, it is best to take equation (7.6) of the main text and solve progressively for all zerocoupon bond prices, starting with year one. This yields the series of zerocoupon bond prices from which we can proceed as usual to determine the yields. Maturity ZeroCoupon Zero Coupon OneYear Par Coupon Cont. Comp. Zero Bond Yield Bond Price Implied Forward Yield Rate 1 0.03000 0.97087 0.03000 0.03000 0.02956 2 0.03500 0.93352 0.04002 0.03491 0.03440 3 0.04000 0.88899 0.05009 0.03974 0.03922 4 0.04700 0.83217 0.06828 0.04629 0.04593 5 0.05300 0.77245 0.07732 0.05174 0.05164 90 Chapter 7 Interest Rate Forwards and Futures Question 7.7. a) We are looking for r ( 1 , 3 ) . We will use equation (7.3) of the main text, and the known oneyear and threeyear zerocoupon bond prices. We have to solve the following equation: 1 + r ( 1 , 3 ) 3 1 = P ( , 1 ) P ( , 3 ) r ( 1 , 3 ) = s P ( , 1 ) P ( , 3 ) 1 = r . 943396 . 816298 1 = . 07504 b) Lets calculate the zerocoupon bond price from year 1 to 2 and from year 1 to 3, they are: P ( 1 , 2 ) = P ( , 2 ) P ( , 1 ) = . 881659 . 943396 = . 93456 P ( 1 , 3 ) = P ( , 3 ) P ( , 1 ) = . 816298 . 943396 = . 86528 Now, we have the relevant implied forward zerocoupon prices and can nd the coupon of the par 2year coupon bond issued at time 1 according to formula (7.6). c = 1 P ( 1 , 3 ) P ( 1 , 2 ) + P ( 1 , 3 ) = . 13472 . 93456 + . 86528 = . 074851 Question 7.8. a) We have to take into account the interest we (or our counterparty) can earn on the FRA settlement if we settle the loan on initiation day, and not on the actual repayment day. Therefore, we tail the FRA settlement by the prevailing market interest rate of 5%. The dollar settlement is: ( r annually r FRA ) 1 + r annually notional principal = ( . 05 . 06 ) 1 + . 05 $500 , 000 . 00 = $4 , 761 . 905 b) If the FRA is settled on the date the loan is repaid (or settled in arrears), the settlement amount is determined by: ( r annually r FRA ) notional principal = ( . 05 . 06 ) $500 , 000 . 00 = $5 , 000 We have to pay at the settlement, because the interest rate we could borrow at is 5%, but we have agreed via the FRA to a borrowing rate of 6%. Interest rates moved in an unfavorable direction. agreed via the FRA to a borrowing rate of 6%....
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This note was uploaded on 12/06/2011 for the course ECON 101 taught by Professor Adam during the Spring '06 term at Neumann.
 Spring '06
 Adam

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