A solution to the market making problem
A solution to the market making problem
复制标题
做市商问题的解决方案
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
J. Fernandez
中科院分区：
文献类型：
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作者：
Olivier Guéant;Charles;J. Fernandez
做市商不断为他们正在考虑的股票设定报价和报价。因此，他们面临着一个复杂的优化问题，基于他们报价的买卖价差和他们确实提供流动性的频率，他们的回报受到了他们因库存而承担的价格风险的挑战。本文考虑一个随机控制问题，类似于Ho和Stoll(17)提出的问题，并由Avellaneda和Stoikov(3)进行了数学形式化。市场模型使用参考价格ST，遵循带有标准差σ的布朗运动，买入或卖出流动性消耗订单的到达率取决于与参考价格ST的距离，做市商在有限时间内最大化其P&L的预期效用。我们证明了与随机最优控制问题相关的Hamilton-Jacobi-Bellman方程可以转化为线性常微分方程组，并解决了库存约束下的做市问题。我们还阐明了最优报价的渐近行为，并提出了闭合形式的近似。
Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization prob- lem in which their return, based on the bid-ask spread they quote and the fre- quency at which they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we consider a stochastic con- trol problem similar to the one introduced by Ho and Stoll (17) and formalized mathematically by Avellaneda and Stoikov (3). The market is modeled using a reference price St following a Brownian motion with standard deviation σ, arrival rates of buy or sell liquidity-consuming orders depend on the distance to the reference price St and a market maker maximizes the expected utility of its P&L over a finite time horizon. We show that the Hamilton-Jacobi-Bellman equations associated to the stochastic optimal control problem can be trans- formed into a system of linear ordinary differential equations and we solve the market making problem under inventory constraints. We also shed light on the asymptotic behavior of the optimal quotes and propose closed-form approxi-