  Trading a financial instrument pushes its price and those of other assets, a
phenomenon known as cross-impact. To be of use, cross-impact models must fit
data and be well-behaved so they can be applied in applications such as optimal
trading. To address these issues, we introduce a set of desirable properties
which constrain cross-impact models. We classify cross-impact models according
to which properties they satisfy and stress them on three different asset
classes to evaluate goodness-of-fit. We find that two models are robust across
markets, but only one satisfies all desirable properties and is appropriate for
applications.
