Show ALL work. Do not use excel.

An FI has a S150 million portfolio of six-year Eurodollar bonds that have an 8 percent 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 -0.632. The underlying long-term Treasury bonds for the option have a duration of 10.2 years and trade at a market value of S94,159 per S100,000 of par value. Each put option has a premium of $3.72 per S100 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