AbstractThis paper proposes a new parsimonious multivariate GARCH–jump (MGARCH–jump) mixture model with multivariate jumps that allows both jump sizes and jump arrivals to be correlated among assets. Dependent jumps impact the conditional moments of returns and beta dynamics of a stock. Applied to daily stock returns, the model identifies co‐jumps well and shows that both jump arrivals and jump sizes are highly correlated. The jump model has better out‐of‐sample forecasts compared with a benchmark multivariate GARCH model.