发表机构
University of Oxford（牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为期权市场做市与返利设计建立嵌套优化模型，求解最优策略，并提出三步返利方案以激励做市商提升流动性，数值实验验证了方案有效性。
AI 中文摘要
我们针对期权市场中做市与返利设计的嵌套优化问题建立了一个模型，并找到了最优策略。一个单一的做市商在局部随机波动率期权市场中交易多种欧式看涨期权，同时采用做市（make）和吃单（take）策略，分别建模为连续控制和脉冲控制。其目标是在所有可行的做市-吃单策略中，最大化期权组合价值与累计返利收入的净收益，同时承担对剩余投资组合的Delta和Vega的惩罚。此外，我们展示了交易所如何通过设定适当的费用返利来激励做市商改善市场流动性，从而解决其自身的流动性吸引问题。为此，我们提出了一种三步返利设计方案，该方案具有灵活性，能够适应交易所设定的特定流动性目标。我们提供了数值结果以验证所提方案的有效性。
英文摘要
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.
