Exercise . (Parallel shifts of the yield curve) The purpose of this exercise is to find out under which assumptions the only possible shifts of the yield curve are parallel, that is such that dy¯τ

t is independent of τ where y¯τ

t = yt+τ t .

(a) Argue that if the yield curve only changes in the form of parallel shifts, then the zero-coupon yields at time t must have the form yT t = yT(rt, t) = rt + h(T − t)

for some function h with h() =  and that the prices of zero-coupon bonds are thereby given as