You are given the following information about one-year interest rates.

t = 0, r_0 = 5.45%

t = 1, r_1,u = 6.17%, r_1,d = 5.05%

t= 2, r_2,uu = 744%, r_2,ud = 6.09%, r_2,dd = 4.99%

Now(t=0) one-year interest rate is 5.45% per year(continuously compounded). Next year the one-year rate will be 6.17% or 5.05% with same probability. if it is 6.17%, the next year of it(t=2) it could be 7.44% or 6.09% with equal probability. If it is 5.05% at t=1, in year two it could be either 6.09% or 4.99% with same probability. All probabilities are risk-neutral probabilities

(1) Let B(t,T) denote the value at time t of a zero-coupon bond pays $1 at time T. at t=0, what is the value ofB(0,1) and B(0,2)?

(2)What is the value of Two-year European Call option wrriten on a one-year zero coupon bond? The pay off to the option at maturity is defind by c(2)=Max{B(2,3)-0.9450,0}

(3) At time 0, please use zero-coupon bonds B(0,1) and B(0,2) to replicate the option.