How Option Hedging Shapes Market Impact

TL;DR

This paper develops a perturbation theory for market impact during option hedging, explaining empirical facts, deriving a pricing equation, and linking immediate and permanent impacts.

Contribution

It extends existing models to include local linear impact and analyzes the effects of hedging metaorders on market dynamics and option pricing.

Findings

Hedging metaorders can explain observed market impact patterns.

Arbitrage opportunities vanish as trading frequency increases.

Relation established between immediate and permanent market impacts.

Abstract

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.