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Neural Hawkes: Non-Parametric Estimation in High Dimension and Causality Analysis in Cryptocurrency Markets 神经霍克斯:加密货币市场中的高维非参数估计和因果关系分析
Pub Date : 2024-01-17 DOI: arxiv-2401.09361
Timothée Fabre, Ioane Muni Toke
We propose a novel approach to marked Hawkes kernel inference which we namethe moment-based neural Hawkes estimation method. Hawkes processes are fullycharacterized by their first and second order statistics through a Fredholmintegral equation of the second kind. Using recent advances in solving partialdifferential equations with physics-informed neural networks, we provide anumerical procedure to solve this integral equation in high dimension. Togetherwith an adapted training pipeline, we give a generic set of hyperparametersthat produces robust results across a wide range of kernel shapes. We conductan extensive numerical validation on simulated data. We finally propose twoapplications of the method to the analysis of the microstructure ofcryptocurrency markets. In a first application we extract the influence ofvolume on the arrival rate of BTC-USD trades and in a second application weanalyze the causality relationships and their directions amongst a universe of15 cryptocurrency pairs in a centralized exchange.
我们提出了一种标记霍克斯核推断的新方法,并将其命名为基于矩的神经霍克斯估计方法。霍克斯过程通过二阶弗里德霍尔积分方程由其一阶和二阶统计量完全定性。利用最近在用物理信息神经网络求解偏微分方程方面取得的进展,我们提供了一个数值程序来求解这个高维积分方程。我们给出了一套通用的超参数,它能在广泛的内核形状中产生稳健的结果。我们在模拟数据上进行了广泛的数值验证。最后,我们提出了该方法在加密货币市场微观结构分析中的两种应用。在第一个应用中,我们提取了交易量对 BTC-USD 交易到达率的影响;在第二个应用中,我们分析了集中式交易所中 15 种加密货币对之间的因果关系及其方向。
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引用次数: 0
Do backrun auctions protect traders? 回流拍卖能保护交易商吗?
Pub Date : 2024-01-16 DOI: arxiv-2401.08302
Andrew W. Macpherson
We study a new "laminated" queueing model for orders on batched tradingvenues such as decentralised exchanges. The model aims to capture andgeneralise transaction queueing infrastructure that has arisen to organise MEVactivity on public blockchains such as Ethereum, providing convenient channelsfor sophisticated agents to extract value by acting on end-user order flow byperforming arbitrage and related HFT activities. In our model, market ordersare interspersed with orders created by arbitrageurs that under idealisedconditions reset the marginal price to a global equilibrium between each trade,improving predictability of execution for liquidity traders. If an arbitrageur has a chance to land multiple opportunities in a row, hemay attempt to manipulate the execution price of the intervening market orderby a probabilistic blind sandwiching strategy. To study how bad thismanipulation can get, we introduce and bound a price manipulation coefficientthat measures the deviation from global equilibrium of local pricing quoted bya rational arbitrageur. We exhibit cases in which this coefficient is wellapproximated by a "zeta value' with interpretable and empirically measurableparameters.
我们研究了一种新的 "层叠 "排队模型,适用于去中心化交易所等分批交易场所的订单。该模型旨在捕捉和概括在以太坊等公共区块链上为组织 MEV 活动而出现的交易排队基础设施,为复杂的代理提供便利的渠道,通过执行套利和相关 HFT 活动,对最终用户订单流采取行动,从而获取价值。在我们的模型中,市场订单中夹杂着套利者创建的订单,在理想化条件下,套利者会在每笔交易之间将边际价格重置为全局均衡价格,从而提高流动性交易者的执行可预测性。如果套利者有机会连续获得多个机会,他可以尝试通过概率盲目夹心策略来操纵介入市场订单的执行价格。为了研究这种操纵的严重程度,我们引入并限定了一个价格操纵系数,用来衡量理性套利者所报的局部定价偏离全局均衡的程度。我们展示了一些案例,在这些案例中,该系数可以很好地通过 "zeta 值 "来近似,而 "zeta 值 "的参数是可解释的,也是经验上可测量的。
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引用次数: 0
Equity auction dynamics: latent liquidity models with activity acceleration 股票拍卖动态:活动加速的潜在流动性模型
Pub Date : 2024-01-12 DOI: arxiv-2401.06724
Mohammed Salek, Damien Challet, Ioane Muni Toke
Equity auctions display several distinctive characteristics in contrast tocontinuous trading. As the auction time approaches, the rate of eventsaccelerates causing a substantial liquidity buildup around the indicativeprice. This, in turn, results in a reduced price impact and decreasedvolatility of the indicative price. In this study, we adapt the latent/revealedorder book framework to the specifics of equity auctions. We provide precisemeasurements of the model parameters, including order submissions,cancellations, and diffusion rates. Our setup allows us to describe the fulldynamics of the average order book during closing auctions in Euronext Paris.These findings support the relevance of the latent liquidity framework indescribing limit order book dynamics. Lastly, we analyze the factorscontributing to a sub-diffusive indicative price and demonstrate the absence ofindicative price predictability.
与连续交易相比,股票拍卖显示出几个与众不同的特点。随着拍卖时间的临近,事件发生的速度加快,导致指示性价格周围的流动性大量增加。这反过来又会降低价格影响,减少指示价格的波动性。在本研究中,我们根据股权拍卖的具体情况调整了潜伏/揭示订单簿框架。我们提供了模型参数的精确测量,包括订单提交、取消和扩散率。这些发现支持了潜在流动性框架在描述限价订单簿动态方面的相关性。最后,我们分析了导致次扩散指示性价格的因素,并证明了指示性价格缺乏可预测性。
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引用次数: 0
A Mean Field Game between Informed Traders and a Broker 知情交易者与经纪人之间的均势博弈
Pub Date : 2024-01-10 DOI: arxiv-2401.05257
Philippe Bergault, Leandro Sánchez-Betancourt
We find closed-form solutions to the stochastic game between a broker and amean-field of informed traders. In the finite player game, the informed tradersobserve a common signal and a private signal. The broker, on the other hand,observes the trading speed of each of his clients and provides liquidity to theinformed traders. Each player in the game optimises wealth adjusted byinventory penalties. In the mean field version of the game, using a G^ateauxderivative approach, we characterise the solution to the game with a system offorward-backward stochastic differential equations that we solve explicitly. Wefind that the optimal trading strategy of the broker is linear on his owninventory, on the average inventory among informed traders, and on the commonsignal or the average trading speed of the informed traders. The Nashequilibrium we find helps informed traders decide how to use privateinformation, and helps brokers decide how much of the order flow they shouldexternalise or internalise when facing a large number of clients.
我们找到了经纪人与平均水平的知情交易者之间随机博弈的闭式解。在有限玩家博弈中,知情交易者观察一个共同信号和一个私人信号。而经纪人则观察每个客户的交易速度,并为知情交易者提供流动性。博弈中的每个参与者都通过库存惩罚来优化财富。在该博弈的均值场版本中,我们使用 G^ateauxderivative 方法,用一个明确求解的前向后向随机微分方程系统来描述博弈解的特征。我们发现,经纪人的最优交易策略与他自己的库存、知情交易者的平均库存以及公共信号或知情交易者的平均交易速度都是线性关系。我们发现的纳什均衡有助于知情交易者决定如何使用私人信息,也有助于经纪商决定在面对大量客户时应该外化还是内化多少订单流。
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引用次数: 0
Scaling Laws And Statistical Properties of The Transaction Flows And Holding Times of Bitcoin 比特币交易流量和持有时间的缩放规律和统计特性
Pub Date : 2024-01-09 DOI: arxiv-2401.04702
Didier Sornette, Yu Zhang
We study the temporal evolution of the holding-time distribution of bitcoinsand find that the average distribution of holding-time is a heavy-tailed powerlaw extending from one day to over at least $200$ weeks with an exponentapproximately equal to $0.9$, indicating very long memory effects. We alsoreport significant sample-to-sample variations of the distribution of holdingtimes, which can be best characterized as multiscaling, with power-lawexponents varying between $0.3$ and $2.5$ depending on bitcoin price regimes.We document significant differences between the distributions of book-to-marketand of realized returns, showing that traders obtain far from optimalperformance. We also report strong direct qualitative and quantitative evidenceof the disposition effect in the Bitcoin Blockchain data. Definingage-dependent transaction flows as the fraction of bitcoins that are traded ata given time and that were born (last traded) at some specific earlier time, wedocument that the time-averaged transaction flow fraction has a power lawdependence as a function of age, with an exponent close to $-1.5$, a valuecompatible with priority queuing theory. We document the existence ofmultifractality on the measure defined as the normalized number of bitcoinsexchanged at a given time.
我们研究了比特币持有时间分布的时间演化,发现持有时间的平均分布是一个重尾幂律,从一天延伸到至少超过 200 美元的星期,指数约等于 0.9 美元,这表明记忆效应非常长。我们还报告了持有时间分布在不同样本间的显著变化,这种变化的最佳特征是多重缩放,根据比特币价格体系的不同,幂律指数在 0.3 美元到 2.5 美元之间变化。我们还报告了比特币区块链数据中处置效应的直接定性和定量证据。我们将与年龄相关的交易流量定义为在给定时间交易的比特币中,在某个特定的较早时间出生(最后一次交易)的比特币的比例,并记录了时间平均交易流量比例与年龄的函数关系为幂律,指数接近$-1.5$,这个值与优先排队理论相一致。我们记录了在特定时间内,定义为比特币兑换归一化数量的量度存在多重折叠性。
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引用次数: 0
Expiring Assets in Automated Market Makers 自动做市商中即将到期的资产
Pub Date : 2024-01-09 DOI: arxiv-2401.04289
Kenan Wood, Maurice Herlihy, Hammurabi Mendes, Jonad Pulaj
An automated market maker (AMM) is a state machine that manages pools ofassets, allowing parties to buy and sell those assets according to a fixedmathematical formula. AMMs are typically implemented as smart contracts onblockchains, and its prices are kept in line with the overall market price byarbitrage: if the AMM undervalues an asset with respect to the market, an"arbitrageur" can make a risk-free profit by buying just enough of that assetto bring the AMM's price back in line with the market. AMMs, however, are not designed for assets that expire: that is, assets thatcannot be produced or resold after a specified date. As assets approachexpiration, arbitrage may not be able to reconcile supply and demand, and theliquidity providers that funded the AMM may have excessive exposure to risk dueto rapid price variations. This paper formally describes the design of a decentralized exchange (DEX)for assets that expire, combining aspects of AMMs and limit-order books. Weensure liveness and market clearance, providing mechanisms for liquidityproviders to control their exposure to risk and adjust prices dynamically inresponse to situations where arbitrage may fail.
自动做市商(AMM)是一种管理资产池的状态机,允许各方根据固定的数学公式买卖这些资产。自动做市商通常以智能合约的形式在区块链上实现,其价格通过套利与整体市场价格保持一致:如果自动做市商相对于市场低估了某项资产的价值,"套利者 "可以通过购买足够多的该资产来使自动做市商的价格与市场价格恢复一致,从而赚取无风险利润。然而,AMM 并不是为过期资产设计的:即在指定日期后无法生产或转售的资产。当资产即将到期时,套利可能无法调和供求关系,为 AMM 提供资金的流动性提供者可能会因价格的快速变化而面临过大的风险。本文结合 AMM 和限价订单簿的各个方面,正式介绍了一种针对到期资产的去中心化交易所(DEX)的设计。我们确保流动性和市场清算,为流动性提供者提供机制来控制风险敞口,并针对套利可能失败的情况动态调整价格。
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引用次数: 0
Optimal Order Execution subject to Reservation Strategies under Execution Risk 执行风险下保留策略的最优订单执行
Pub Date : 2024-01-06 DOI: arxiv-2401.03305
Xue Cheng, Peng Guo, Tai-ho Wang
The paper addresses the problem of meta order execution from abroker-dealer's point of view in Almgren-Chriss model under order filluncertainty. A broker-dealer agency is authorized to execute an order oftrading on client's behalf. The strategies that the agent is allowed to deployis subject to a benchmark, referred to as the reservation strategy, regulatedby the client. We formulate the broker's problem as a utility maximizationproblem in which the broker seeks to maximize his utility of excessprofit-and-loss at the execution horizon. Optimal strategy in feedback form isobtained in closed form. In the absence of execution risk, the optimalstrategies subject to reservation strategies are deterministic. We establish anaffine structure among the trading trajectories under optimal strategiessubject to general reservation strategies using implementation shortfall andtarget close orders as basis. We conclude the paper with numerical experimentsillustrating the trading trajectories as well as histograms of terminal wealthand utility at investment horizon under optimal strategies versus those underTWAP strategies.
本文从经纪自营商的角度出发,探讨了 Almgren-Chriss 模型中订单填充不确定性下的元订单执行问题。经纪商代理被授权代表客户执行交易指令。允许代理部署的策略受制于客户规定的基准(称为保留策略)。我们将经纪人的问题表述为一个效用最大化问题,在这个问题中,经纪人寻求最大化其在执行期的超额利润和损失的效用。以封闭形式获得反馈形式的最优策略。在没有执行风险的情况下,受制于保留策略的最优策略是确定的。我们以执行缺口和目标平仓单为基础,建立了在一般保留策略下最优策略的交易轨迹结构。最后,我们通过数值实验展示了最优策略与 TWAP 策略下的交易轨迹,以及投资期末财富和效用的柱状图。
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引用次数: 0
Forecasting Bitcoin Volatility: A Comparative Analysis of Volatility Approaches 预测比特币波动性:波动率预测方法比较分析
Pub Date : 2024-01-04 DOI: arxiv-2401.02049
Cristina Chinazzo, Vahidin Jeleskovic
This paper conducts an extensive analysis of Bitcoin return series, with aprimary focus on three volatility metrics: historical volatility (calculated asthe sample standard deviation), forecasted volatility (derived from GARCH-typemodels), and implied volatility (computed from the emerging Bitcoin optionsmarket). These measures of volatility serve as indicators of marketexpectations for conditional volatility and are compared to elucidate theirdifferences and similarities. The central finding of this study underscores anotably high expected level of volatility, both on a daily and annual basis,across all the methodologies employed. However, it's crucial to emphasize thepotential challenges stemming from suboptimal liquidity in the Bitcoin optionsmarket. These liquidity constraints may lead to discrepancies in the computedvalues of implied volatility, particularly in scenarios involving extrememoneyness or maturity. This analysis provides valuable insights into Bitcoin'svolatility landscape, shedding light on the unique characteristics and dynamicsof this cryptocurrency within the context of financial markets.
本文对比特币收益率序列进行了广泛分析,主要关注三个波动率指标:历史波动率(按样本标准差计算)、预测波动率(由 GARCH 模型得出)和隐含波动率(由新兴的比特币期权市场计算得出)。这些波动率衡量指标作为市场对条件波动率的预期指标,通过比较来阐明它们之间的异同。这项研究的核心发现强调,在所有采用的方法中,无论是按日还是按年计算,波动率的预期水平都非常高。然而,强调比特币期权市场流动性不理想所带来的潜在挑战是至关重要的。这些流动性限制可能会导致隐含波动率计算值的差异,尤其是在涉及极端资金或期限的情况下。这项分析为了解比特币的波动率情况提供了宝贵的见解,揭示了这种加密货币在金融市场背景下的独特特征和动态。
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引用次数: 0
Opinion formation in the world trade network 世界贸易网络中的舆论形成
Pub Date : 2024-01-04 DOI: arxiv-2401.02378
Célestin Coquidé, José Lages, Dima L. Shepelyansky
We extend the opinion formation approach to probe the world influence ofeconomical organizations. Our opinion formation model mimics a battle betweencurrencies within the international trade network. Based on the United NationsComtrade database, we construct the world trade network for the years of thelast decade from 2010 to 2020. We consider different core groups constituted bycountries preferring to trade in a specific currency. We will considerprincipally two core groups, namely, 5 Anglo-Saxon countries which prefer totrade in US dollar and the 11 BRICS+ which prefer to trade in a hypotheticalcurrency, hereafter called BRI, pegged to their economies. We determine thetrade currency preference of the other countries via a Monte Carlo processdepending on the direct transactions between the countries. The resultsobtained in the frame of this mathematical model show that starting from year2014 the majority of the world countries would have preferred to trade in BRIthan USD. The Monte Carlo process reaches a steady state with 3 distinctgroups: two groups of countries preferring, whatever is the initialdistribution of the trade currency preferences, to trade, one in BRI and theother in USD, and a third group of countries swinging as a whole between USDand BRI depending on the initial distribution of the trade currencypreferences. We also analyze the battle between USD, EUR and BRI, and presentthe reduced Google matrix description of the trade relations between theAnglo-Saxon countries and the BRICS+.
我们扩展了舆论形成方法,以探究经济组织的世界影响力。我们的舆论形成模型模拟了国际贸易网络中的货币之争。基于联合国贸易数据库,我们构建了从 2010 年到 2020 年这十年间的世界贸易网络。我们考虑了由倾向于使用特定货币进行贸易的国家构成的不同核心集团。我们主要考虑两个核心集团,即 5 个盎格鲁-撒克逊国家和 11 个 "金砖+"国家,前者更倾向于使用美元进行贸易,后者更倾向于使用与其经济挂钩的假定货币进行贸易,以下称为 "金砖倡议"。我们根据国家间的直接交易,通过蒙特卡洛过程确定其他国家的贸易货币偏好。在此数学模型框架下得出的结果表明,从 2014 年开始,世界上大多数国家都倾向于使用 BRI 而非美元进行贸易。蒙特卡洛过程达到的稳态有三组不同的国家:两组国家,无论贸易货币偏好的初始分布如何,都倾向于使用 BRI 和美元进行贸易;第三组国家,根据贸易货币偏好的初始分布,整体上在美元和 BRI 之间摇摆。我们还分析了美元、欧元和金砖国家之间的竞争,并提出了盎格鲁-撒克逊国家与金砖国家+之间贸易关系的谷歌矩阵描述。
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引用次数: 0
Deep Reinforcement Learning for Quantitative Trading 量化交易的深度强化学习
Pub Date : 2023-12-25 DOI: arxiv-2312.15730
Maochun Xu, Zixun Lan, Zheng Tao, Jiawei Du, Zongao Ye
Artificial Intelligence (AI) and Machine Learning (ML) are transforming thedomain of Quantitative Trading (QT) through the deployment of advancedalgorithms capable of sifting through extensive financial datasets to pinpointlucrative investment openings. AI-driven models, particularly those employingML techniques such as deep learning and reinforcement learning, have showngreat prowess in predicting market trends and executing trades at a speed andaccuracy that far surpass human capabilities. Its capacity to automate criticaltasks, such as discerning market conditions and executing trading strategies,has been pivotal. However, persistent challenges exist in current QT methods,especially in effectively handling noisy and high-frequency financial data.Striking a balance between exploration and exploitation poses another challengefor AI-driven trading agents. To surmount these hurdles, our proposed solution,QTNet, introduces an adaptive trading model that autonomously formulates QTstrategies through an intelligent trading agent. Incorporating deepreinforcement learning (DRL) with imitative learning methodologies, we bolsterthe proficiency of our model. To tackle the challenges posed by volatilefinancial datasets, we conceptualize the QT mechanism within the framework of aPartially Observable Markov Decision Process (POMDP). Moreover, by embeddingimitative learning, the model can capitalize on traditional trading tactics,nurturing a balanced synergy between discovery and utilization. For a morerealistic simulation, our trading agent undergoes training usingminute-frequency data sourced from the live financial market. Experimentalfindings underscore the model's proficiency in extracting robust marketfeatures and its adaptability to diverse market conditions.
通过部署先进的算法,人工智能(AI)和机器学习(ML)正在改变量化交易(QT)领域,这些算法能够通过广泛的金融数据集筛选出有利的投资机会。人工智能驱动的模型,特别是那些采用深度学习和强化学习等人工智能技术的模型,在预测市场趋势和执行交易方面表现出了巨大的优势,其速度和准确性远远超过了人类的能力。其自动执行关键任务的能力,如辨别市场行情和执行交易策略,一直都是至关重要的。然而,当前的 QT 方法仍然存在挑战,尤其是在有效处理嘈杂的高频金融数据方面。为了克服这些障碍,我们提出的解决方案 QTNet 引入了一种自适应交易模型,通过智能交易代理自主制定 QT 策略。通过将深度强化学习(DRL)与模仿学习方法相结合,我们提高了模型的能力。为了应对波动性金融数据集带来的挑战,我们在部分可观测马尔可夫决策过程(POMDP)的框架内对 QT 机制进行了概念化。此外,通过嵌入定量学习,该模型可以利用传统的交易策略,在发现和利用之间形成平衡的协同效应。为了进行逼真的模拟,我们的交易代理使用来自实时金融市场的分钟频率数据进行训练。实验结果表明,该模型能熟练地提取稳健的市场特征,并能适应不同的市场条件。
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引用次数: 0
期刊
arXiv - QuantFin - Trading and Market Microstructure
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