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Liquidity Provision and Rebate Design in Option Markets

Author

Listed:
  • Samuel N. Cohen
  • Lyndon Drake
  • Zihan Guo
  • Christoph Reisinger

Abstract

We provide a model for the nested optimisation problem of market making and rebate design problems in option markets and find optimal strategies. A single market maker trades multiple European call options in a local-stochastic volatility option market with both make and take strategies, modeled, respectively, as continuous and impulse controls. Her objective is to maximize, over all admissible make-take strategies, net profit of option portfolio value and cumulative rebate revenue, subject to a penalty on residual portfolio delta and vega. In addition, we demonstrate how an exchange can incentivize a market maker to improve market liquidity by setting suitable fee rebates, thereby resolving its own liquidity attraction problem. To this end, we propose a three-step rebate design scheme with flexibility to accommodate specific liquidity targets imposed by an exchange. Numerical results are provided to validate the effectiveness of the proposed scheme.

Suggested Citation

  • Samuel N. Cohen & Lyndon Drake & Zihan Guo & Christoph Reisinger, 2026. "Liquidity Provision and Rebate Design in Option Markets," Papers 2609.26606, arXiv.org.
    • Handle: RePEc:arx:papers:2609.26606
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    References listed on IDEAS

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