Option market making with hedging-induced market impact

TL;DR

This paper models how option market making activities influence underlying asset prices through hedging-induced market impact, combining stochastic demand with permanent and transient effects.

Contribution

It introduces a coupled model of option demand and market impact, analyzes manipulation/arbitrage, and develops a numerical method for optimal quoting strategies.

Findings

Market manipulation and arbitrage can occur due to feedback effects.

The model captures the interplay between liquidity, inventory risk, and impact.

Numerical strategies approximate optimal quoting in complex impact scenarios.

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.