A pension fund plans to buy $10,000,000 worth of annual-coupon bond A in 1 month, which currently yields 5% per annum. Bond A has a duration of 10 years. The fund is worried about the\ change in interest rate, and would like to have a hedge with an option position on bonds. An\ available call contract currently has a price of $1.5 per $100 face value of bonds, while an available\ put contract has a price of $2.1 per $100 face value of bonds. Delta is 0.5 for the calls and 0.6\ for the puts.\ (a) [2 points] Suppose the fund would like to buy options to hedge the bonds, should it buy calls\ or puts? Why?\ (b) [2 points] Based on (a), suppose the underlying bond of the option contracts happens to yield 5%\ 6\ with a duration of 10 years, has a price of 102% of the face value, and is subject to the same change\ in yields as bond A. Each option contract is on 100 units of underlying bonds (each bond has a face\ value of $1,000), how many options should the fund buy? Assume fractions of options are available.\ (c) [2 points] What are the total cost of the option position in (b)?