  We present a perturbation theory of the market impact based on an extension
of the framework proposed by [Loeper, 2018] -- originally based on [Liu and
Yong, 2005] -- in which we consider only local linear market impact. We study
the execution process of hedging derivatives and show how these hedging
metaorders can explain some stylized facts observed in the empirical market
impact literature. As we are interested in the execution process of hedging we
will establish that the arbitrage opportunities that exist in the discrete time
setting vanish when the trading frequency goes to infinity letting us to derive
a pricing equation. Furthermore our approach retrieves several results already
established in the option pricing literature such that the spot dynamics
modified by the market impact. We also study the relaxation of our hedging
metaorders based on the fair pricing hypothesis and establish a relation
between the immediate impact and the permanent impact which is in agreement
with recent empirical studies on the subject.
