The current term-structure of risk-free rate is as follows.

Term-structure in year 0, when the maturity is year 1, the zero-rate is 2.5%, when the maturity is year 2, the zero-rate is 3.0%.

A risk-free bond will pay $1,000 two years from now. The price of the bond one year later depends on the term structure then. There are two possible scenarios in year 1:

Term-structure in year 1 , for Scenario A, when the maturity is year 1, the zero rate is 1%. Term-structure in year 1, for Scenario A, when the maturity is year 2, the zero rate is 2%.

Term-structure in year 1 , for Scenario B, when the maturity is year 1, the zero rate is 4%. Term-structure in year 1, for Scenario B, when the maturity is year 2, the zero rate is 5%.

An investor considers buying an one-year European call option on the bond with the strike price of $970.

(a) What are the payoffs in scenario A and B in year one for a long position in the call?

(b) What is the present value (in year 0) of the call? (Hint: Find a replicating portfolio using the two-year bond and an one-year bond. For an one-year bond, you can choose any face value as you like.)