  Trading a financial asset pushes its price as well as the prices of other
assets, a phenomenon known as cross-impact. We consider a general class of
kernel-based cross-impact models and investigate suitable parameterisations for
trading purposes. We focus on kernels that guarantee that prices are
martingales and anticipate future order flow (martingale-admissible kernels)
and those that ensure there is no possible price manipulation
(no-statistical-arbitrage-admissible kernels). We determine the overlap between
these two classes and provide formulas for calibration of cross-impact kernels
on data. We illustrate our results using SP500 futures data.
