2. You are given the following risk-neutral interest rate tree for continuously compounded interest rates with a step-size of A=1 year: t = 0 (i = 0) t = 1 = (i 1) t= 2 (i = 2) T2,uu = 0.06 T1,u 0.055 To = 0.05 T2,ud = 12,du = 0.05 r1,d = 0.047 T2,dd = 0.045 The risk-neutral probability to move up or down the tree is equals to 0.5. 1 (a) Compute the value of an interest rate swap at t = 0, from the perspective of a fixed rate payer, for a 3 year interest rate swap with a swap rate of 5% and a notional value of 100. (b) Compute the t = 0 price of a 3 year interest rate floor with strike rate 5% and a notional value of 100. (c) Compute the value of a 3 year callable bond with principal of 100, and a 5.25% coupon that is paid annually (i.e. at time t = 1, 2, 3). =