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Common affine term structure models (ATSMs) suggest that bond yields include both expected short rates and term premiums, in violation of the strictest forms of the expectations hypothesis (EH). Similarly, forward foreign exchange contracts likely include not only expected depreciation but also a sizeable premium, which similarly contradicts pure interest rate parity (IRP) and complicates inferences about anticipated returns on foreign currency exposure. Closely following the underlying logic of ubiquitous term structure models in parallel, and rather than the usual econometric approach, this study derives arbitrage-free affine forward currency models (AFCMs) with closed-form expressions for both unobservable variables. Model calibration to eleven forward U.S. dollar currency pair term structures, and notably without any information from corresponding term structures, from the mid-to-late 1990s through early 2015 fits the data closely and suggests that the premium is indeed nonzero and variable, but not to the degree implied by previous econometric studies.