Question: Need help for PART E ... Thanks PART E Consider an insurance company that needs to pay out 10 million in each of the years

Need help for PART E ... Thanks

PART E

Consider an insurance company that needs to pay out 10 million in each of the years t = 4 and t = 5. The term structure is currently flat at 5% per year. The firm's assets at t = 0 consist of cash, and net worth is zero. a. Compute the present value of the firm's liabilities. b. If the term structure goes down by 0.5% while remaining flat, what would be the new net worth of the firm? c. Compute the modified duration of the firm's liabilities. Compute the approximate change y in the value of liabilities using modified duration. Suppose, the firm decides to invest all its assets only in one zero-coupon bond with maturity T and face value pound 100. What should be the maturity T of this bond to hedge the interest rate risk? e. Suppose, in year 0 the firm invested all cash in the bond described in part d, the interest rate remained flat at 5% throughout year 1. In the beginning of year 1 the firm again decides to hedge against the interest rate risks. Solve problems in parts a, b, c and d from the perspective of year 1. Consider an insurance company that needs to pay out 10 million in each of the years t = 4 and t = 5. The term structure is currently flat at 5% per year. The firm's assets at t = 0 consist of cash, and net worth is zero. a. Compute the present value of the firm's liabilities. b. If the term structure goes down by 0.5% while remaining flat, what would be the new net worth of the firm? c. Compute the modified duration of the firm's liabilities. Compute the approximate change y in the value of liabilities using modified duration. Suppose, the firm decides to invest all its assets only in one zero-coupon bond with maturity T and face value pound 100. What should be the maturity T of this bond to hedge the interest rate risk? e. Suppose, in year 0 the firm invested all cash in the bond described in part d, the interest rate remained flat at 5% throughout year 1. In the beginning of year 1 the firm again decides to hedge against the interest rate risks. Solve problems in parts a, b, c and d from the perspective of year 1

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