Optimal pair-trade execution with generalized cross-impact
Optimal pair-trade execution with generalized cross-impact
复制标题
具有广义交叉影响的最佳配对交易执行
DOI：
10.1007/s10690-021-09349-1
复制
发表时间：
2021
影响因子：
1.7
通讯作者：
Makoto Shimoshimizu
中科院分区：
文献类型：
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作者：
Masamitsu Ohnishi;Makoto Shimoshimizu
我们研究具有广义交叉影响的离散时间最优配对交易执行问题。这项研究是 Fukasawa 等人的延伸。 （2020b），它考虑了具有马尔可夫依赖性的小交易者提出的总随机订单对价格的影响。我们关注的是规避风险的大型交易者如何以最佳方式执行两种相关资产，以在有限的范围内最大化他/她从终端财富中获得的预期效用。马尔可夫决策过程模型构成了制定最优配对交易执行问题的基础。然后，在某些规律性条件下，动态规划的后向归纳法使我们能够推导出最优的配对交易执行策略及其相关的最优价值函数。小交易者对每种风险资产的交易订单确实会影响两种风险资产的最佳执行量。此外，模拟实验的数值结果表明，交叉影响会影响最优执行策略，并且在我们的交叉影响模型设置下，存在大型交易者利用“统计”套利并增加其预期效用的往返交易。
We examine a discrete–time optimal pair–trade execution problem with generalized cross–impact. This research is an extension of Fukasawa et al. (2020b), which considers the price impact of aggregate random orders posed by small traders with a Markovian dependence. We focus on how a risk–averse large trader optimally executes two correlated assets to maximize his/her expected utility from the terminal wealth over a finite horizon. A Markov decision process modeling constitutes the basis for the formulation of the optimal pair–trade execution problem. Then, under some regularity conditions, the backward induction method of dynamic programming enables us to derive the optimal pair–trade execution strategy and its associated optimal value function. The trading orders of each risky asset posed by small traders do affect the optimal execution volume of both risky assets. Moreover, numerical results with simulation experiments show that the cross–impact affects the optimal execution strategy and a round–trip trade exists for the large trader to utilize a ‘statistical’ arbitrage and to increase his/her expected utility under our model setting of cross–impact.