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

Real-world forward rate dynamics with affine realizations