where ∧ denotes exterior product. The above expression is the exterior product of M two-forms of rank two, which produces a volume form D2,2(v1, . . . , v4M ) in the 2M -dimensional linear space. If we fix a basis e1, . . . , e2M in the linear space, then each of the vectors vi can be expressed as a sequence of 2M numbers, and D2,2(v1, . . . , v4M ) is also a number (the coefficient at e1∧. . ....

This work studies the information content of trades in world’s largest over-the-counter (OTC) market, foreign exchange (FX) market. It analyzes a novel, comprehensive order flow data set, distinguishing among different groups market participants and covering large cross-section currency pairs. We find compelling evidence heterogeneous superior across agents, time, pairs, consistent with asymmet...