The current term-structure of risk-free rate is as follows. Term-structure in year 0 maturity (years) zero-rate (%) 1 2.5 2 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 Scenario A Scenario B maturity (years) zero-rate (%) maturity (years) zero-rate (%) 1 1.0 1 4.0 2 2.0 2 5.0 An investor considers buying an one-year European call option on the bond with the strike price of $970. (a) What are the payos in scenario A and B in year one for a long position in the call? [6 points] (b) What is the present value (in year 0) of the call? [7 points] (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.)