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 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.)