Let F t (T 0 ,T i ) denote the forward price at time t for buying

Question:

Let F_t(T₀,T_i) denote the forward price at time t for buying at time T₀ a unit-par zero-coupon bond with maturity T_i. Show that the forward swap rate [see (7.1.4)] can be expressed as

.[To, Th] = - 1 F,(, ) = ; F,(T;, )

where α_i is the accrual factor of the period [T_i₋₁,T_i]. Alternatively, suppose we write the forward LIBOR as L_i(t) = L_t[T_i₋₁,T_i]. By observing that

B(t, Tk) B(t, To) k = [] i=1 = B(t, Ti) B(t, Ti-1) k = [] i=1 = arva 1 + ; Li (t)' k 1, show that the forward swap rate can be expressed as