You are given the following one-step interest rate tree: t = 0 (i = 0) t = 0.5 (i = 1) r0 = 0.02 r1,u = 0.04 with probability p = 0.5 r1,d = 0.01 with probability p = 0.5 The rates are expressed in continuously compounded terms. In addition, the 1 year ZCB is trading at $97.4845 at t = 0. (a) What is the expected 6 month treasury rate E [r1]? (b) What is the market price of risk ? (c) Compute the risk neutral probability for an upward movement in the interest rate. (d) Option A has payoff given by 100 max {r1 0.02, 0} at t = 0.5. i. Compute the price of option A at t = 0. ii. Construct a replicating portfolio for option A using 6 month and 1 year ZCBs.