  We introduce a linear cross-impact framework in a setting in which the price
of some given financial instruments (derivatives) is a deterministic function
of one or more, possibly tradeable, stochastic factors (underlying). We show
that a particular cross-impact model, the multivariate Kyle model, prevents
arbitrage and aggregates (potentially non-stationary) traded order flows on
derivatives into (roughly stationary) liquidity pools aggregating order flows
traded on both derivatives and underlying. Using E-Mini futures and options
along with VIX futures, we provide empirical evidence that the price formation
process from order flows on derivatives is driven by cross-impact and confirm
that the simple Kyle cross-impact model is successful at capturing
parsimoniously such empirical phenomenology. Our framework may be used in
practice for estimating execution costs, in particular hedging costs.
