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  3. a) a derivative contract pays lt [t, t + ] at time

a) A derivative contract pays LT [T, T + ] at time T + ....

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Finance

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 at t T of the derivative contract is Z(t,T)Z(t,T +).

b) LetT0,T1,...Tn beasequenceoftimes,withTi+1 =Ti+foraconstant>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 =0andasn.

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