  We investigate the existence of affine realizations for L\'{e}vy driven
interest rate term structure models under the real-world probability measure,
which so far has only been studied under an assumed risk-neutral probability
measure. For models driven by Wiener processes, all results obtained under the
risk-neutral approach concerning the existence of affine realizations are
transferred to the general case. A similar result holds true for models driven
by compound Poisson processes with finite jump size distributions. However, in
the presence of jumps with infinite activity we obtain severe restrictions on
the structure of the market price of risk; typically, it must even be constant.
