Question

A 2-year 10% annual coupon bond of a company is trading at $1066.14 per $1000 face value. A 2-year zero coupon bond of the same issuer is trading at $907.03 per $1000 face value. Use no-arbitrage arguments to find what should be the price of a 1-year zero coupon bond of the same issuer for $100 face value?

Answer 1

2 year zero coupon bond price = 907.03

Face value = 1000

Price = Face value / (1+S2)^2

So

S2 = (1000/907.03)^(1/2) - 1 = 4.9999 % = 5%

2 year coupon bond price = 1066.14

Coupon rate = 10%

Face value = 1000

coupon payment = 1000 * 0.1 = 100

Let say 1 year zero coupon rate = S1

So

Price of coupon bond = coupon / (1+S1) + coupon / (1+S2)^2 + Face value / (1+S2)^2

(This method is called bootstrapping)

1066.14 = 100 / (1+S1) + 1100 /(1.05)^2

So

S1 = 46.18%

So 1 year zero coupon bond price

Price = 100 / (1.4618) = 68.40

let me know if you have any doubts