This paper shows that jumps in financial asset prices are often erroneously identified and are, in fact, rare events accounting for a very small proportion of the total price variation. We apply new econometric techniques to a comprehensive set of ultra high-frequency equity and foreign exchange tick data recorded at millisecond precision, allowing us to examine the price evolution at the individual order level. We show that in both theory and practice, traditional measures of jump variation based on lower-frequency data tend to spuriously assign a burst of volatility to the jump component. As a result, the true price variation coming from jumps is overstated. Our estimates based on tick data suggest that the jump variation is an order of magnitude smaller than typical estimates found in the existing literature.