This paper studies bivariate tail comovements on financial markets that are of crucial importance for the world economy: the S&P 500, US bonds, and currencies. We propose to study that form of dependence under the lens of cojump identification in a bivariate Brownian semimartingale with idiosyncratic jumps, as well as cojumps. Whereas univariate jump identification has been widely studied in the high-frequency data literature, the multivariate literature on cojump identification is more recent and scarcer. Cojump identification is of interest, as it may identify comovements which are not trivially visible in a univariate setting. That is, price changes can be small relative to local variation, but still abnormal relative to local covariation. This paper investigates how simple parametric bootstrapping of the product of assets' intraday returns can help detect cojumps in a multivariate Brownian semi-martingale with both idiosyncratic jumps and cojumps. In particular, we investigate how to disentangle idiosyncratic jumps from common jumps at an intraday level for pairs of assets. The approach is flexible, trivial to implement, and yields good power properties. It allows to shed new light on extreme dependence at the world economy level. We detect cojumps of heterogeneous size which are partly undetected with a univariate approach. We find an increased cojump intensity after the crisis on the S&P 500-US bonds pair before a return to normal.