Option market making with hedging-induced market impact

Paulin Aubert (), Etienne Chevalier () and Vathana Ly Vath ()
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Paulin Aubert: LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Etienne Chevalier: LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Vathana Ly Vath: UEVE - Université d'Évry-Val-d'Essonne

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Abstract: This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker's quoted prices. The resulting dynamics combine stochastic option demand with both permanent and transient impact on the underlying, leading to a coupled evolution of inventory and price. We first study market manipulation and arbitrage phenomena that may arise from the feedback between option trading and underlying impact. We then establish the well-posedness of the mixed control problem, which involves continuous quoting decisions and impulsive hedging actions. Finally, we implement a numerical method based on policy optimization to approximate optimal strategies and illustrate the interplay between option market liquidity, inventory risk, and underlying impact.

Keywords: Option market making; Cox processes; Mixed stochastic control; Policy optimization; Machine learning (search for similar items in EconPapers)
Date: 2026-05-25
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Published in Applied Mathematical Finance, 2026, ⟨10.1080/1350486X.2026.2671725⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05641417

DOI: 10.1080/1350486X.2026.2671725

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