You are given the following one-step interest rate tree: t = 0.5 (i = 1) T1,u = 0.04 with probability p = 0.5| Tid = 0.01 with probability p = 0.5 T1,d t=0 (i=0) To = 0.02 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[r]? (b) What is the market price of risk X? (c) Compute the risk neutral probability for an upward movement in the interest rate. (d) Option A has payoff given by 100 x max{r -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.