Consider the following bonds: Bond LUKE is a 3-year bearing coupon bond of 5% every six-months with a face value of $1,000. Coupon payments of $50 are made every 6 months. Bond ROUGE is a 3-year bearing coupon bond of 12% per year with a face value of $1,000. Coupon payments of $120 are made every 12 months. Suppose that the yield on the bond is 6% per annum with continuous compounding.

a) Calculate the bonds price, duration & convexity.

b) Regarding TSIR: explain the meaning of duration. According to the Liquidity Preference Theory, which is the best option for a trader for a 3-years investment? LUKE or ROUGE? Justify your answer.

c) How would you price the bond LUKE if the yield curve fell down 100 basis points (continuous compounding)?

d) How much is the modified duration regarding a rate in semi-annual compounding?