An FI has purchased a two-year, $1,000 par value zero-coupon bond for $907.03. 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 5% and the one-year rate in one year is forecast to be either 4.5% or 5.5% 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.

(a) What is the expected one-year interest rate, one year before the maturity of the bond?

(b) What is the expected price of the bond if it has to be sold one year before the maturity of the bond?

(c) If the FI buys a call option with an exercise price equal to your answer in part (b), what will be the premium on the call option today?

(d) Effect of Volatility on Option Prices: 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 4% and 6%?