Corporate Bank has $ 840 million of assets with a duration of 12 years and liabilities worth

Question:

Corporate Bank has $ 840 million of assets with a duration of 12 years and liabilities worth $ 720 million with a duration of seven years. Assets and liabilities are yielding 7.56 percent. The bank is concerned about preserving the value of its equity in the event of an increase in interest rates and is contemplating a macrohedge with interest rate options. The call and put options have a of $ 100,000, are priced at 1 44/64 and 56/64, respectively, and have a delta (d) of 0.4 and – 0.4, respectively. The price of an underlying T-bond is 104.53125 (104 68/128), its duration is 8.17 years, and its yield to is 7.56 percent.
a. What type of option should Corporate Bank use for the macrohedge?
b. How many options should be purchased?
c. What is the effect on the economic value of the equity if interest rates rise 50 basis points?
d. What is the dollar change in value of the option position if interest rates rise by 50 basis points?
e. What will be the cost of the hedge if each option has a premium of $ 0.875 per $ 100 of
f. How much must interest rates move against the hedge for the increased value of the bank to offset the cost of the hedge?
g. How much must interest rates move in favor of the hedge, or against the balance sheet, before the payoff from the hedge will exactly cover the cost of the hedge?

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