Consider the following coupon bonds with face value $100 and annual coupon rate C as reported in the table below:

Bond

A

B

C

respectively

Maturity (years)

1

2

3

respectively

Coupon C

4%

5%

6%

respectively

Yield to maturity

5.051%

6.092%

6.377%

respectively

a) Using the given yields to maturity calculate the spot rates r0,1 r0,2 and r0,3 for 1 to 3 years maturity respectively

b) Consider a coupon bond D with face value of $100, time to maturity of 3 years and coupon rate C=5.5 %.What is the theoretical (arbitrage free) price of bond D?

c) Suppose that bonds A, B, C are traded at their fair prices, while bond D is currently trading at a market price of $90 Explain why there is an arbitrage opportunity and how to construct it in order to make profits. Show detailed calculations and positions in the various bonds and also the arbitrage profit made

d) Compute the forward rate for a 2 years investment starting in 1 year using the spot interest rates.