Liquidity Provision and Rebate Design in Option Markets

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.