Hedging Interest Rate Risk with Options: A FI has a $200 million portfolio of six-year Eurodollar bonds that have an 5% coupon. The bonds are trading at par and have a duration of five years. The FI wishes to hedge the portfolio with T-bond options that have a delta of -0.625. The underlying long-term Treasury bonds for the option have a duration of 8.25 years and trade at a market value of $94,000 per $100,000 of par value. Each put option has a premium of $2.5 per $100 of face value.

(a) How many bond put options are necessary to hedge the bond portfolio?

(b) What is the total cost of placing the hedge?

(c) How far must interest rates move before the payoff on the hedge will exactly offset the cost of placing the hedge?