Assuming that the forward rates f
are semimartingales, we give conditions on their components under which the discounted bond prices are martingales. To achieve this, we give sufficient conditions for the integrated processes f
dv to be semimartingales, and identify their various components. We recover the no-arbitrage conditions in models well known in the literature and, finally, we formulate a new random field model for interest rates and give its equivalent martingale measure (no-arbitrage) condition.