Optimal high-frequency trading with limit and market orders
Optimal high-frequency trading with limit and market orders
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DOI：
10.1080/14697688.2012.708779
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发表时间：
2011-06
影响因子：
1.3
通讯作者：
Fabien Guilbaud;H. Pham
中科院分区：
文献类型：
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作者：
Fabien Guilbaud;H. Pham
我们提出了一个框架，研究最优的市场决策在限价订单簿（LOB）。买卖价差的LOB是由一个滴答值连续时间马尔可夫链建模。我们考虑一个小型代理人，他不断地以最佳买入/卖出报价提交限价买入/卖出订单，并且也可能以最佳买入/卖出报价设置限价订单（分别为：问）加（分别为减）一个用于获得执行指令优先级的报价，这是高频交易中的一个关键问题。代理人面临执行风险，因为她的限价单只有在与对应的市价单相符时才被执行。由于持有风险资产时价格波动，她还面临库存风险。然后，代理人也可以选择以市价订单进行交易，从而获得立即执行，但价格较低。做市商的目标是在控制库存的同时，通过在限价委托和市价委托之间进行权衡，使其在短期内的预期效用最大化。这是制定为一个混合政权切换定期/脉冲控制问题，我们的特点是在一个准变分系统的动态规划方法。校准程序推导出估计的过渡矩阵和强度参数的蔓延和考克斯过程建模的执行限制订单。我们提供了一个明确的向后分裂计划解决这个问题，并显示它可以减少到一个简单的方程组，只涉及库存和传播变量。在模拟和真实的数据上进行了几个计算测试，并说明了在限价订单和市价订单中考虑执行优先级时的影响和利润。
We propose a framework for studying optimal market-making policies in a limit order book (LOB). The bid–ask spread of the LOB is modeled by a tick-valued continuous-time Markov chain. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at best bid (resp. ask) plus (resp. minus) a tick for obtaining execution order priority, which is a crucial issue in high-frequency trading. The agent faces an execution risk since her limit orders are executed only when they meet counterpart market orders. She is also subject to inventory risk due to price volatility when holding the risky asset. The agent can then also choose to trade with market orders, and therefore obtain immediate execution, but at a less favorable price. The objective of the market maker is to maximize her expected utility from revenue over a short-term horizon by a trade-off between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/impulse control problem that we characterize in terms of a quasi-variational system by dynamic programming methods. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. We provide an explicit backward splitting scheme for solving the problem and show how it can be reduced to a system of simple equations involving only the inventory and spread variables. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market orders.