Let rt denote the short rate at time t and suppose we have an affine term structure model so that

where A(t, T) and B(t, T) are deterministic functions of time t and maturity T.
(a) Let f (t; s, s + δ) denote the forward rate at time t for lending between times s and s+δ, where t 0. Compute an expression for f (t; s, s + δ) in terms of rt and the functions A(., .) and B(., .).
(b) Let rs(s + δ) denote the spot rate at time s for lending or borrowing out to time s+δ. Give an expression for rs(s+δ) in terms of rs and the function A(., .) and B(., .).

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(21.97)