For an IBM bond with 6% coupon rate (annual coupon payment), two year to maturity, par value of $1,000, and selling at $1018. Assume that one-year rates undergo a lognormal random walk with volatility s, and s is assumed to be 12%. It is given that the one-year spot rate today is 5.03%.

a) Calculate the one-year forward rate one year from now in low state using binomial model.

b) Calculate the value of the IBM bond in the question if the coupon rate changes to 7% using binomial model.

c) Calculate the value of the IBM bond in the question assuming it is callable at price of $1000.

d) Calculate the value of the IBM bond in the question assuming it is putable at price of $1000.