Use the change-of-num?raire toolkit and the DC-operator to derive the drift of the n-th forward LIBOR under the spot LIBOR measure Q_B, for an arbitrary time 0 ? t n?1. Keep in mind that the process X_t in the definition of B_d(t) in Problem 21.1 is almost surely constant.

Problem 21.1

Suppose that the tenor structure T?₁, T₀, . . . , T_N is equispaced, with ?t = T_n ? T_n?1 and T_?1 = 0. For 0 ? t ? T_N, the discretely rebalanced bank account B_d(t) has present value.

with

where ?(x) is again the Heaviside-?-function. Use Theorem 17.2 on page 390 to prove that X_t has the dynamics

Transcribed Image Text:

Ba(1) = X,PN,(1), %3D N-1 N, X, = [] and N, = 0(t - T„), n=0 P„(Tn-1) n=0