Use this list of Treasury bond prices as of February 15, 2001 to answer the foll
ID: 2417244 • Letter: U
Question
Use this list of Treasury bond prices as of February 15, 2001 to answer the following questions.
Coupon
8s
0s
6s
10s
Maturity
8/15/01
8/15/02
8/15/02
2/15/02
Quote
101
91.5
100
?
(a) Derive the 6-month, 1-year and 1.5-year discount factors using the 8s, 0s and 6s.
(b) What is the arbitrage-free price for the 10s given the discount factors from (a).
(c) Compute the 6-month, 1-year and 1.5-year par yields.
(d) Based on the no-arbitrage principle, compute the forward rates from 6 months to 1.5 years and 1 year to 1.5 years.
(e) Construct a synthetic forward loan from 6 months to 1.5 years using the 8s and 0s. Solve for the positions in the bonds and verify that the loan rate equals the forward rate of the same term.
(f) Construct a synthetic forward loan from 1 year to 1.5 years using the 8s, 0s and 6s. Solve for the positions in the bonds and verify that the loan rate equals the forward rate of the same term.
Coupon
8s
0s
6s
10s
Maturity
8/15/01
8/15/02
8/15/02
2/15/02
Quote
101
91.5
100
?
Explanation / Answer
Use this list of Treasury bond prices as of February 15, 2001 to answer the following questions.
(a) Derive the 6-month, 1-year and 1.5-year discount factors using the 8s, 0s and 6s.
(b) What is the arbitrage-free price for the 10s given the discount factors from (a).
(d) Based on the no-arbitrage principle, compute the forward rates from 6 months to 1.5 years and 1 year to 1.5 years.
(e) Construct a synthetic forward loan from 6 months to 1.5 years using the 8s and 0s. Solve for the positions in the bonds and verify that the loan rate equals the forward rate of the same term.
(f) Construct a synthetic forward loan from 1 year to 1.5 years using the 8s, 0s and 6s. Solve for the positions in the bonds and verify that the loan rate equals the forward rate of the same term.
2. Arbitrage free price @ 10% = Pv(10%/2,1,0,-100) = $95.24
Use this list of Treasury bond prices as of February 15, 2001 to answer the following questions.
Coupon Maturity Quote 8s 15/8/01 101 0s 15/8/02 91.5 6s 15/8/02 100 10s 15/2/02 ?(a) Derive the 6-month, 1-year and 1.5-year discount factors using the 8s, 0s and 6s.
(b) What is the arbitrage-free price for the 10s given the discount factors from (a).
(c) Compute the 6-month, 1-year and 1.5-year par yields.(d) Based on the no-arbitrage principle, compute the forward rates from 6 months to 1.5 years and 1 year to 1.5 years.
(e) Construct a synthetic forward loan from 6 months to 1.5 years using the 8s and 0s. Solve for the positions in the bonds and verify that the loan rate equals the forward rate of the same term.
(f) Construct a synthetic forward loan from 1 year to 1.5 years using the 8s, 0s and 6s. Solve for the positions in the bonds and verify that the loan rate equals the forward rate of the same term.
a. 6 months coupon rate = 8%/2 =4% Face value = $100 Total value of bond after 6 months = $100 + $4 104 Present Value 100 Discount factor = 101 = 104 (d .5) 0.961538462 Discount factor (d .5) 0.96154 97.115 1 year coupon rate 8% Face value = $100 Total value of bond after 1 year = $100 + $8 108 Present Value 100 Discount factor = 101 = 108 (d 8%) Discount factor (d 8%) 0.92593 ($96.15) For Example 8%= 8%/2 = 4% 6 months = 1/(1+4%)^1 = 0.9615 1 year= 1/(1+4%)^2 = 0.9246 1.5 year =1/(1+4%)^3 = 0.8890 6 months 1 year 1.5 years Coupon Quote (PV) FV = $100 + 4 x1 FV = $100 + 4 x2 FV = $100 + 4 x3 8% 101 $104.00 108 112 Discount Factor 0.9712 0.9352 0.9018 0% 91.5 Discount Factor = 91.5/104,91.5/108,91.5/112 0.8798 0.8472 0.8170 6% 100 0.9615 0.9259 0.8929 2)Compute the 6-month, 1-year and 1.5-year par yields 6 months 1 year 1.5 year PV Coupon Face Value PMT Yield 101 8% $100 $4 2.97% 3.47% 3.64% 91.5 0% 100 $0 9.29% 4.54% 3.01% 100 6% 100 $3 3.00% 3.00% 3.00%Related Questions
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