Consider the following bonds: Bond "LUKE" is a 3-year bearing coupon bond of 10% every six-months with a face value of $1,000. Coupon payments of $100 are made every 6 months. Bond "ROUGE" is a 3-year bearing coupon bond of 20% per year with a face value of $1,000. Coupon payments of $200 are made every 12 months. Suppose that the yield on the bond is 10% per annum with continuous compounding. a) Calculate the bond's 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 goes up to 50 basis points (continuous compounding)? d) How much is the modified duration regarding a rate in semi-annual compounding