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A note on Almgren-Chriss optimal execution problem with geometric Brownian motion 几何布朗运动下Almgren-Chriss最优执行问题的注释
Pub Date : 2020-06-19 DOI: 10.1142/s2382626620500057
Bastien Baldacci, J. Benveniste
We solve explicitly the Almgren-Chriss optimal liquidation problem where the stock price process follows a geometric Brownian motion. Our technique is to work in terms of cash and to use functional analysis tools. We show that this framework extends readily to the case of a stochastic drift for the price process and the liquidation of a portfolio.
我们明确地解决了股票价格过程遵循几何布朗运动的Almgren-Chriss最优清算问题。我们的技术是根据现金来工作,并使用功能分析工具。我们表明,这个框架很容易扩展到价格过程的随机漂移和投资组合清算的情况。
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引用次数: 1
Novel insights in the Levy–Levy–Solomon agent-based economic market model 列维-列维-所罗门代理经济市场模型的新见解
Pub Date : 2020-02-13 DOI: 10.1142/s0129183121500200
Maximilian Beikirch, T. Trimborn
The Levy-Levy-Solomon model (A microscopic model of the stock market: cycles, booms, and crashes, Economic Letters 45 (1))is one of the most influential agent-based economic market models. In several publications this model has been discussed and analyzed. Especially Lux and Zschischang (Some new results on the Levy, Levy and Solomon microscopic stock market model, Physica A, 291(1-4)) have shown that the model exhibits finite-size effects. In this study we extend existing work in several directions. First, we show simulations which reveal finite-size effects of the model. Secondly, we shed light on the origin of these finite-size effects. Furthermore, we demonstrate the sensitivity of the Levy-Levy-Solomon model with respect to random numbers. Especially, we can conclude that a low-quality pseudo random number generator has a huge impact on the simulation results. Finally, we study the impact of the stopping criteria in the market clearance mechanism of the Levy-Levy-Solomon model.
列维-列维-所罗门模型(股票市场的微观模型:周期,繁荣和崩溃,经济快报45(1))是最有影响力的基于主体的经济市场模型之一。在一些出版物中,对该模型进行了讨论和分析。特别是Lux和Zschischang(关于Levy, Levy和Solomon微观股票市场模型的一些新结果,Physica A, 291(1-4))表明该模型具有有限尺寸效应。在这项研究中,我们在几个方向上扩展了现有的工作。首先,我们展示了揭示模型的有限尺寸效应的模拟。其次,我们阐明了这些有限尺寸效应的起源。此外,我们证明了Levy-Levy-Solomon模型对随机数的敏感性。特别是,我们可以得出结论,低质量的伪随机数生成器对仿真结果有很大的影响。最后,我们研究了停止标准在Levy-Levy-Solomon模型的市场出清机制中的影响。
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引用次数: 0
Allocation Discretion, Information Sharing and Underwriter Syndication 分配自由裁量权、信息共享和承销商联合
Pub Date : 2018-07-20 DOI: 10.2139/ssrn.3217770
N. Parikh, V. Marisetty, M. Tan
The competitiveness of the IPO underwriting market suffers from the concentration of restricted mandates in the hands of a limited number of underwriters with good reputations. Academic research has focused extensively on the relationship between underpricing and the influence of an individual underwriter. However, we have only scant research on the effect of IPO syndication on underpricing. Nevertheless, most IPOs are managed by underwriters operating as an IPO syndicate. Here, we contribute to an analysis of underwriting syndicates by examining 329 IPOs issued in the Indian IPO market in the period 2000-10 that were made subject to either a discretionary or a proportionate allocation regime. We find that the underwriting market in India is highly concentrated and is dominated by a few large and reputable underwriters who have ongoing relationships amongst themselves to manage IPOs. This highlights a potential entry barrier for new underwriters. We find that underwriters form large syndicates when the issue size is large. Also, we do not find any evidence that the motivation for underwriters to form a syndicate is due to market risk sharing or price manipulation. We conclude that underwriters syndicate to share the inventory risk of an IPO. When allocation discretion is regulated, and the risk of managing an IPO is high, we observe that the size of an underwriting syndicate is smaller. However, the results support the role of institutional subscription acting as a mediating factor for reputable underwriters to syndicate. Able to share the risk in this way, the syndicate partnership benefits the issuer with lower underpricing. Overall, we conclude that regulatory intervention is positive for market welfare due to lower underpricing. We also find that in the absence of allocation discretion, syndication by reputable underwriters acts as an effective medium of discretion for higher information and risk sharing.
IPO承销市场的竞争力受到影响,因为有限的委托委托集中在数量有限、声誉良好的承销商手中。学术研究广泛关注定价过低与单个承销商影响力之间的关系。然而,我们对IPO联合对股价过低影响的研究很少。然而,大多数IPO都是由作为IPO辛迪加运作的承销商管理的。本文通过对2000- 2010年期间在印度IPO市场发行的329宗IPO进行分析,分析了承销团的情况,这些IPO均采用酌情分配或比例分配制度。我们发现,印度的承销市场高度集中,并由少数几家信誉良好的大型承销商主导,这些承销商之间一直保持着管理ipo的关系。这凸显了新承销商可能面临的进入障碍。我们发现,当发行规模较大时,承销商会形成大型辛迪加。此外,我们没有发现任何证据表明承销商组建辛迪加的动机是由于市场风险分担或价格操纵。我们得出结论,承销商辛迪加分担库存风险的IPO。当分配自由裁量权受到监管,且管理IPO的风险较高时,我们观察到承销团的规模较小。然而,研究结果支持机构认购在信誉良好的承销商进行辛迪加的中介作用。辛迪加合伙能够以这种方式分担风险,以较低的低定价使发行人受益。总体而言,我们得出的结论是,由于低定价,监管干预对市场福利是积极的。我们还发现,在缺乏分配自由裁量权的情况下,由信誉良好的承销商组成的辛迪加作为一种有效的自由裁量权媒介,可以获得更高的信息和风险分担。
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引用次数: 0
Order-book modelling and market making strategies 订单模型和做市策略
Pub Date : 2018-06-01 DOI: 10.1142/S2382626619500035
Xiaofei Lu, F. Abergel
Market making is one of the most important aspects of algorithmic trading, and it has been studied quite extensively from a theoretical point of view. The practical implementation of so-called "optimal strategies" however suffers from the failure of most order book models to faithfully reproduce the behaviour of real market participants. This paper is twofold. First, some important statistical properties of order driven markets are identified, advocating against the use of purely Markovian order book models. Then, market making strategies are designed and their performances are compared, based on simulation as well as backtesting. We find that incorporating some simple non-Markovian features in the limit order book greatly improves the performances of market making strategies in a realistic context.
做市是算法交易中最重要的方面之一,从理论角度对其进行了广泛的研究。然而,所谓“最优策略”的实际实施,受到大多数订单簿模型未能忠实再现真实市场参与者行为的影响。这篇论文是双重的。首先,确定了订单驱动市场的一些重要统计属性,反对使用纯粹的马尔可夫订单簿模型。然后,在模拟和回测的基础上,设计了做市策略并对其性能进行了比较。我们发现,在限价单中加入一些简单的非马尔可夫特征,极大地提高了现实环境下做市策略的性能。
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引用次数: 9
Dynamical regularities of US equities opening and closing auctions. 美国股票开盘和收盘拍卖的动态规律。
Pub Date : 2018-02-01 DOI: 10.1142/S2382626619500011
D. Challet, Nikita Gourianov
We first investigate static properties of opening and closing auctions such as typical auction volume relative to daily volume and order value distributions. We then show that the indicative match price is strongly mean-reverting because the imbalance is, which we link to strategic behavior. Finally, we investigate how the final auction price reacts to order placement, especially conditional on imbalance improving or worsening events and find a large difference between the opening and closing auctions, emphasizing the role of liquidity and simultaneous trading in the pre-open or open-market order book.
我们首先研究了开盘和收盘拍卖的静态特性,例如相对于每日交易量和订单价值分布的典型拍卖量。然后我们表明,指示性匹配价格是强烈的均值回归,因为不平衡是,我们将其与战略行为联系起来。最后,我们研究了最终拍卖价格对订单分配的反应,特别是在不平衡改善或恶化事件的条件下,发现开盘和收盘拍卖之间存在很大差异,强调了流动性和同步交易在预开盘或公开市场订单簿中的作用。
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引用次数: 3
How Facebook Drives Investor Behavior Facebook如何驱动投资者行为
Pub Date : 2017-09-22 DOI: 10.2139/SSRN.3040621
Milla Siikanen, K. Baltakys, H. Kärkkäinen, J. Jussila, Ravikiran Vatrapu, R. Mukkamala, Abid Hussain, J. Kanniainen
Recent studies combining social media data with data from capital markets have mainly focused on the relationship between returns and activity on social media. In contrast, we study how behavior of different investor categories are associated to Facebook posts and other activity on a company's Facebook wall. We provide evidence that the decisions of less sophisticated investors---namely, households and nonprofit organizations---to increase or decrease their shareholdings are associated with Facebook data, while the decisions of more sophisticated investors---financial and insurance institutions---are not associated with Facebook data.
最近将社交媒体数据与资本市场数据相结合的研究主要集中在回报与社交媒体活动之间的关系上。相比之下,我们研究了不同投资者类别的行为如何与Facebook帖子和公司Facebook墙上的其他活动相关联。我们提供的证据表明,不太成熟的投资者(即家庭和非营利组织)增持或减持股份的决定与Facebook数据有关,而更成熟的投资者(金融和保险机构)的决定与Facebook数据无关。
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引用次数: 1
Behind the Price: On the Role of Agent’s Reflexivity in Financial Market Microstructure 价格背后:代理人反身性在金融市场微观结构中的作用
Pub Date : 2017-08-08 DOI: 10.1007/978-3-319-49872-0_3
P. Barucca, F. Lillo
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引用次数: 2
Order Flows and Limit Order Book Resiliency on the Meso-Scale 中观尺度上的订单流和限制订单弹性
Pub Date : 2017-08-01 DOI: 10.1142/S2382626618500065
Kyle Bechler, M. Ludkovski
We investigate the behavior of limit order books on the meso-scale motivated by order execution scheduling algorithms. To do so we carry out empirical analysis of the order flows from market and limit order submissions, aggregated from tick-by-tick data via volume-based bucketing, as well as various LOB depth and shape metrics. We document a nonlinear relationship between trade imbalance and price change, which however can be converted into a linear link by considering a weighted average of market and limit order flows. We also document a hockey-stick dependence between trade imbalance and one-sided limit order flows, highlighting numerous asymmetric effects between the active and passive sides of the LOB. To address the phenomenological features of price formation, book resilience, and scarce liquidity we apply a variety of statistical models to test for predictive power of different predictors. We show that on the meso-scale the limit order flows (as well as the relative addition/cancellation rates) carry the most predictive power. Another finding is that the deeper LOB shape, rather than just the book imbalance, is more relevant on this timescale. The empirical results are based on analysis of six large-tick assets from Nasdaq.
我们研究了由订单执行调度算法驱动的限价订单在中观尺度上的行为。为此,我们对来自市场和限价订单提交的订单流进行了实证分析,并通过基于量的分类,以及各种LOB深度和形状指标,从逐点数据中汇总。我们记录了贸易不平衡和价格变化之间的非线性关系,然而,通过考虑市场和限价订单流量的加权平均,可以将其转换为线性联系。我们还记录了贸易不平衡和单边限价订单流动之间的曲棍球棒依赖关系,突出了LOB主动和被动双方之间的许多不对称效应。为了解决价格形成、账面弹性和稀缺流动性的现象学特征,我们应用各种统计模型来测试不同预测者的预测能力。我们表明,在中尺度上,限价订单流(以及相对的加/取消率)具有最大的预测能力。另一个发现是,更深层次的LOB形状,而不仅仅是账面不平衡,在这个时间尺度上更相关。实证结果是基于对纳斯达克六大大额资产的分析得出的。
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引用次数: 7
Instantaneous order impact and high-frequency strategy optimization in limit order books 限价订单中的瞬时订单影响和高频策略优化
Pub Date : 2017-07-01 DOI: 10.1142/S2382626618500016
Federico Gonźalez, M. Schervish
We propose a limit order book (LOB) model with dynamics that account for both the impact of the most recent order and the shape of the LOB. We present an empirical analysis showing that the type of the last order significantly alters the submission rate of immediate future orders, even after accounting for the state of the LOB. To model these effects jointly we introduce a discrete Markov chain model. Then on these improved LOB dynamics, we find the policy for optimal order choice and placement in the share purchasing problem by framing it as a Markov decision process. The optimal policy derived numerically uses limit orders, cancellations and market orders. It looks to exploit the state of the LOB summarized by the volume at the bid/ask and the type of the most recent order to obtain the best execution price, avoiding non-execution and adverse selection risk simultaneously. Market orders are used aggressively when the mid-price is expected to move adversely. Limit orders are placed under favorable LOB conditions and canceled when non-execution or adverse selection probability is high. Using ultra high-frequency data from the NASDAQ stock exchange we compare our optimal policy with other submission strategies that use a subset of all available order types and show that ours significantly outperforms them.
我们提出了一个动态的限价订单(LOB)模型,该模型考虑了最近订单的影响和LOB的形状。我们提出了一项实证分析,表明即使考虑了LOB的状态,最后订单的类型也会显著改变近期订单的提交率。为了模拟这些效应,我们引入了一个离散马尔可夫链模型。然后,在这些改进的LOB动力学上,我们通过将股票购买问题构建为马尔可夫决策过程,找到了最优订单选择和放置策略。数值推导的最优策略使用限价单、取消单和市价单。它寻求利用由买卖量和最近订单类型总结的LOB状态,以获得最佳执行价格,同时避免不执行和逆向选择风险。当预期中间价格走势不利时,市场订单被积极使用。限价订单在有利的LOB条件下下,当不执行或逆向选择概率高时取消。使用来自纳斯达克股票交易所的超高频数据,我们将我们的最佳策略与使用所有可用订单类型子集的其他提交策略进行比较,并表明我们的策略明显优于它们。
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引用次数: 8
Limit Order Strategic Placement with Adverse Selection Risk and the Role of Latency 具有逆向选择风险的限价单策略配售及潜伏期的作用
Pub Date : 2016-10-02 DOI: 10.1142/S2382626617500095
Charles-Albert Lehalle, Othmane Mounjid
This paper is split in three parts: first we use labelled trade data to exhibit how market participants accept or not transactions via limit orders as a function of liquidity imbalance; then we develop a theoretical stochastic control framework to provide details on how one can exploit his knowledge on liquidity imbalance to control a limit order. We emphasis the exposure to adverse selection, of paramount importance for limit orders. For a participant buying using a limit order: if the price has chances to go down the probability to be filled is high but it is better to wait a little more before the trade to obtain a better price. In a third part we show how the added value of exploiting a knowledge on liquidity imbalance is eroded by latency: being able to predict future liquidity consuming flows is of less use if you have not enough time to cancel and reinsert your limit orders. There is thus a rational for market makers to be as fast as possible as a protection to adverse selection. Thanks to our optimal framework we can measure the added value of latency to limit orders placement. To authors' knowledge this paper is the first to make the connection between empirical evidences, a stochastic framework for limit orders including adverse selection, and the cost of latency. Our work is a first stone to shed light on the roles of latency and adverse selection for limit order placement, within an accurate stochastic control framework.
本文分为三个部分:首先,我们使用标记的交易数据来展示市场参与者如何通过限价单接受或不接受交易作为流动性失衡的函数;然后,我们建立了一个理论随机控制框架,详细说明了如何利用流动性不平衡的知识来控制限价单。我们强调暴露于逆向选择,对限价订单至关重要。对于使用限价单购买的参与者:如果价格有机会下跌,则补仓的可能性很高,但最好在交易前再等待一段时间,以获得更好的价格。在第三部分中,我们展示了利用流动性失衡知识的附加值是如何被延迟所侵蚀的:如果你没有足够的时间取消和重新插入限价单,那么能够预测未来流动性消耗流的作用就会减弱。因此,作为对逆向选择的一种保护,做市商尽可能快地行动是合理的。由于我们的最优框架,我们可以衡量延迟的附加价值,以限制订单的放置。据作者所知,本文是第一个将经验证据、包含逆向选择的限价订单随机框架和延迟成本联系起来的论文。我们的工作是在精确的随机控制框架内阐明延迟和逆向选择在限价订单放置中的作用的第一块石头。
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引用次数: 40
期刊
arXiv: Trading and Market Microstructure
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