Abstract This paper presents some asset pricing results for the general case in which asset prices can jump. Asset gains (price plus cumulative dividends) processes are assumed to be special semimartingales. This is the broadest class of processes for which local risk premia exist. The risk premium can be separated into a premium for the continuous part of the return and a premium for the jump part. The jump premium is non-zero only for jumps which occur simultaneously with jumps in the state price density process. The CCAPM holds if consumption rates vary continuously with time, in which case all jump risks are unpriced. More generally, the CCAPM always characterizes the continuous part of the security return.