Please answer all of these questions completely from A to D. Would be appreciated if tutor can do that as it is allowed to do 4 subpart questions . Thanks

1. This question is about bonds, arbitrage, and immunization. a) marks consider two bonds, both with face value E100. The coupons are paid annually. Bond 1 is a three-year 20% bond and bond 2 is a three-year 10% bond. Bond 1 is traded at a price of E132 and bond 2 at a price of 106. In addition to these bonds, a three-year 15% bond is traded at a price of 120. Is there an arbitrage opportunity? If so, design an arbitrage strategy that generates a net profit of 100. b) marks] What is the discount factor da implied by the prices of bonds 1 and 2 from part a? Suppose now, in addition to bonds 1 and 2 a two-year zero with face value 100 is traded at a price of 85. What are the discount factors d1, d2, and da in the latter case? c) 15 marks]A pension fund expects to pay 2 1, and its payments will grow at a rate of million in year g 1% in perpetuity in all subsequent years. The value of assets is equal to 50 million. The structure is flat at r 9%. How many 15-year zero coupon bonds with face value 100 does the company need to buy to immunize the liabilities? Does the firm have a sufficient amount of money? modified duration of perpetuities with growth is given by D's1/(-g)l. [Hint the d) [6 marks) Discuss the intuition behind the immunization strategy. Why might pension funds and insurance companies go bankrupt when interest rates decrease? Is it possible to perfectly immunize an infinite stream of liabilities, such as in part c)? Explain