Find the price at t0nbspof the floating rate bond - using a

Question

Floating rate bond Let T₀, T₁, ... , Tn be a sequence of times with T_i+1 = T_{i + α} for a constant α > 0. A floating rate bond with notional 1, start date T₀ and maturity T_n pays libor coupons of αL_Ti [T_i, T_{i + α}] at times T_i+1, for i = 0, ... , n - 1, and notional 1 at T_n.

(a) Find the price at t₀ of the floating rate bond.

(b) Using a replication argument, find the forward price at t for the floating rate bond (for a forward contract with maturity T), t₀.