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5) We now consider another specific form of the martingale model (2)-the Cox-Ingersoll-Ross (CIR) model: dr (t) = a(b - r(t) ) dt +ovr(t)dW(t). (4) 2 a) Suppose that the term structure is given by FT (t, T) = Ao(T - t)e-B(T-t), te [0, T]. Show that Ao and B must satisfy the following system of differential equations: B' (t ) + aB (t ) + 502 B2 ( t ) - 1 = 0 Ab(t) + abB(t) Ao(t) = 0, (5) Ao(0) = 1, B(0) = 0. b) Solve the ODEs to show that 2(evt - 1) 2 ye( aty ) (t / 2 ) 2ab/o2 B(t) = ( 7 + a) (ert - 1) + 2y' Ao(t) = L(y + a)(ert - 1) + 27] where y = va2 + 202. (Note, if you cannot solve the ODEs, then at least verify that the given functions are the solutions to (5) to get partial credits.) c) Define Y(t) = Vr(t), t 2 0. Derive the dynamics of Y