Exercise . (HJM with USV) Let the risk-neutral forward rate dynamics be given by df T t

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Exercise . (HJM with USV) Let the risk-neutral forward rate dynamics be given by df T t = ˆα (t, T, vt) dt + √vte

−κ[T−t] dzQ

t ,  ≤ t ≤ T, where dvt = μv(vt) dt + σv(vt) dzQ

t

, and z Q

 and z Q

 are independent standard Brownian motions under Q.

(a) Show that

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