This paper extends a popular no‐arbitrage affine term structure model to jointly model bond markets and exchange rates across the UK, USA and euro area. Using a monthly data set of forward rates from 1992, we first demonstrate that two global factors account for a significant proportion in the variation of bond yields across countries. We also show that, for an explanation of country‐specific movements in yield curves, local factors are required. Although we implement a very general factor structure, we find that our global factors are related to global inflation and global economic activity, whereas local factors are closely linked to monetary policy rates. In this respect, our results are similar to previous work. But an important advantage of our joint international model is that we are able to decompose interest rates into risk‐free rates and risk premia. Additionally, we are able to study the implications for exchange rates. We show that whereas differences in risk‐free rates matter, to a large extent, changes in the exchange rate are determined by time‐varying exchange rate risk premia. Copyright © 2013 John Wiley & Sons, Ltd.