a) A derivative contract pays LT [T , T + ] at time T + . By constructing a portfolio of ZCBs and a libor deposit that replicates the payout, prove that the value attT of the derivative contract is Z(t,T)Z(t,T+).

b) Let T0, T1,...Tn be a sequence of times, with Ti+1 =Ti+ for a constant >0. Use your results from (a) to show that a floating leg of libor payments LTi [Ti, Ti + ] at times Ti+1, i = 0,1,...,n 1, has value at time t T0 equal to a simple linear combination of ZCB prices.

c) Hence find the value of a spot-starting infinite stream of libor payments, that is, when t = T0 =0 and as n.