Brown National Bank (BNB) has $780 million in assets earning an average rate of 6.75%. BNB’s duration gap is -1.46 years, and BNB wants to hedge this gap using options on Treasury securities.

a) What position in options should BNB take (buy calls, buy puts, sell calls, sell puts) to hedge its interest rate risk exposure? Explain how your position works to hedge BNB’s risk.

b) BNB chooses to use options on 8% 10-year Treasury notes with face value of $100,000 per contract, duration of 6.3 years, and a price of $107,675 per contract. The call option delta (δ) is 0.85; the put option delta is –0.7. How many of these option contracts will be required for BNB to hedge?

Which are are the correct answers and the way to solve them?