Find the value of a spot starting infinite stream

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Reference no: EM131243619

Floating rate annuity

(a) A derivative contract pays αL_T[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 at t ≤ T of the derivative contract is Z(t, T) - Z(t, T + α).

(b) Let T₀, T₁, ... , T_n be a sequence of times, with T_i+1 = T_{i + α} for a constant α > 0. Use your result from (a) to show that a floating leg of libor payments αL_Ti [T_i, T_i + α] at times T_i+1, i = 0, 1, ... , n - 1, has value at time t ≤ T₀ equal to a simple linear combination of ZCB prices.

Reference no: EM131243619

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