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做市商利润激励与Kyle模型的相变

文章 arXiv papers · 作者: Charles-Albert Lehalle et al.
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总结

本文修改了Kyle知情交易框架，对知情交易者、噪声交易者和做市商之间的互动进行建模。知情交易者选择市价单规模，随后做市商根据合并后的订单流为资产定价。做市商的目标函数还纳入了与订单流和买卖价差相关的额外收入项。

作者推导出知情交易者收入最大化的交易，并给出均衡成立的充分条件，同时使用神经网络方法检验均衡是否成立。随着做市商收入项的权重变化，模型产生三种定价状态：无价差的线性规则、有价差的线性中间价，以及中间价为零且价差较大的亚稳态。这些是理论模型结果；说明中未提供实证市场检验，也未说明这些状态在多大范围内适用。

核心观点

  • 模型在做市商的目标函数中加入与价差和订单流相关的收入项。
  • 知情交易者先选择订单规模，做市商再根据总订单流设定价格。
  • 本文推导知情交易者的最优交易选择和均衡成立的充分条件。
  • 研究使用神经网络验证所提出的均衡。
  • 做市商收入激励变化会产生三种不同的定价状态。

标签

做市市场微观结构统计学机器学习
全文
# Phase Transitions in Kyle's Model with Market Maker Profit Incentives


# Phase Transitions in Kyle's Model with Market Maker Profit Incentives









We consider a stochastic game between three types of players: an inside trader, noise traders and a market maker. In a similar fashion to Kyle's model, we assume that the insider first chooses the size of her market-order and then the market maker determines the price by observing the total order-flow resulting from the insider and the noise traders transactions. In addition to the classical framework, a revenue term is added to the market maker's performance function, which is proportional to the order flow and to the size of the bid-ask spread. We derive the maximizer for the insider's revenue function and prove sufficient conditions for an equilibrium in the game. Then, we use neural networks methods to verify that this equilibrium holds. We show that the equilibrium state in this model experience interesting phase transitions, as the weight of the revenue term in the market maker's performance function changes. Specifically, the asset price in equilibrium experience three different phases: a linear pricing rule without a spread, a pricing rule that includes a linear mid-price and a bid-ask spread, and a metastable state with a zero mid-price and a large spread.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。