We model asset prices in the most general sensible form as special semimartingales. This approach allows us to also include jumps in the asset price process. We show that the existence of an equivalent martingale measure, which is essentially equivalent to no-arbitrage, implies that the asset prices cannot exhibit predictable jumps. Hence, in arbitrage-free markets the occurrence and the size of any jump of the asset price cannot be known before it happens. In practical applications it is basically not possible to dis- tinguish between predictable and unpredictable discontinuities in the price process. The empirical literature has typically assumed as an identification condition that there are no predictable jumps. Our result shows that that identification condition follows from the existence of an equivalent martingale measure, and hence essentially comes for free in arbitrage-free markets.