a) Build a binomial tree if the current one-year spot rate is r1 = 4%, two-year spot rate is r2 = 5%, and three-year spot rate is r3 = 6%. In addition, it is estimated that the volatility of the current one-year spot rate is 3% and that one year from now the volatility of the one-year spot rate will be 3%. Assume that the risk-neutral probabilities are p = 1 p = 0.5.

b) find the price of the at-the-money call option on the three-year bond with option maturity equal to two years.