Abstract The nature of the dependence between discontinuities in prices and contemporaneous discontinuities in volatility (co-jumps) has been reported by many as being elusive, in terms of sign, magnitude, and statistical significance. Using a novel identification strategy in continuous time relying on trade-level information for spot variance estimation, as well as infinitesimal cross-moments, we document that a sizeable proportion of discontinuous changes in prices are associated with strongly anti-correlated, contemporaneous, discontinuous changes in volatility. Assuming a possibly nonmonotonic pricing kernel, we illustrate the equilibrium implications of price and volatility co-jumps for return and variance risk premia.