  Trading a financial asset pushes its price as well as the prices of other
assets, a phenomenon known as cross-impact. The empirical estimation of this
effect on complex financial instruments, such as derivatives, is an open
problem. To address this, we consider a setting in which the prices of
derivatives is a deterministic function of stochastic factors where trades on
both factors and derivatives induce price impact. We show that a specific
cross-impact model satisfies key properties which make its estimation tractable
in applications. Using E-Mini futures, European call and put options and VIX
futures, we estimate cross-impact and show our simple framework successfully
captures some of the empirical phenomenology. Our framework for estimating
cross-impact on derivatives may be used in practice for estimating hedging
costs or building liquidity metrics on derivative markets.
