# insurance company that needs to pay out £10 million in each of the years

## Question: insurance company that needs to pay out £10 million in each of the years

- Consider an insurance company that needs to pay out £10 million in each of the years t=4 and t=5. The term stricture is currently flat at 5% per year. The firm’s assets at t=0 consist cash, and its net worth is zero.
- Compute the present value of the firm’s liabilities.
- If the term structure goes down by 0.5% while remaining flat, what would be the new net worth of the firm?
- Compute the modified duration of the firm’s liabilities. Compute the approximate change 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 £100. What should he the maturity T of this bond to hedge the interest rate risk?
- 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.