An FI has purchased a two-year, $1,000 par value zero-coupon bond for $867.43. The FI will hold the bond to maturity unless it needs to sell the bond at the end of one year for liquidity purposes. The current one-year interest rate is 7 percent and the one-year rate in one year is forecast to be either 8.04 percent or 7.44 percent with equal likelihood. The FI wishes to buy a put option to protect itself against a capital loss if the bond needs to be sold in one year.

What is the yield on the bond at the time of purchase?

What is the market-determined, implied one-year rate one year before maturity?

What is the expected sale price if the bond has to be sold at the end of one year?

Diagram the bond prices over the two-year horizon.

page 767If the FI buys a put option with an exercise price equal to your answer in part (c), what will be its value at the end of one year?

What should be the premium on the put option today?

Diagram the value of the put option on the two-year, zero-coupon bond.

What would have been the premium on the option if the one-year interest rates at the end of one year were expected to be 8.14 percent and 7.34 percent?