a) A derivative contract pays LT [T , T + ] at time T + . By constructing a portfolio of ZCBs and a libor

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

b) Let T0, T1,...Tn be a sequence of times, with Ti+1 =Ti+α for a constant α>0. Use your results from (a) to show that a floating leg of libor payments αLTi [Ti, Ti + α] 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→∞.