Suppose you are given the following information about the default-free coupon-paying yield curve:

QUESTION

Suppose you are given the following information about the default-free, coupon-paying yield curve: Maturity (years) 1 2 3 4 Coupon rate (annual payments) 0.00% 10.00% 6.00% 12.00% YTM 2.000% 3.908% 5.840% 5.783% a. Use arbitrage to determine the yield to maturity of a two-year, zero-coupon bond. b. What is the zero-coupon yield curve for years 1 through 4?
a. Cash flow in year 1 2 3 4 2 year coupon bond ($1000 face value) 100 1100 Less 1 year bond ($100 face value) -100 Two year zero ($1100 face value) 0 1100 Price of 2 year coupon bond 1115.05 Price of 1 year bond 98.04 Price of 2 year (0)=(Price of 2 year coupon bond) (price of one year bond) 1017.01 YTM(2 year 0) 4.000% Price of 2

year coupon bond = 100/(1+0.03908) + 1000/(1+0.03908)^2 = $1115.05 Price of 1 year coupon bond = 100/(1+2.000%)=$98.04 Price of 2 year (0)=(Price of 2 year coupon bond) (price of one year bond) = 1115.05-98.04=$1017.01 b.

ANSWER:

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