Pub Date : 2023-04-15DOI: 10.1142/s2382626620500136
P. Wu, M. Rambaldi, J. Muzy, E. Bacry
{"title":"A single queue reactive Hawkes model for the order flow","authors":"P. Wu, M. Rambaldi, J. Muzy, E. Bacry","doi":"10.1142/s2382626620500136","DOIUrl":"https://doi.org/10.1142/s2382626620500136","url":null,"abstract":"","PeriodicalId":232544,"journal":{"name":"Market Microstructure and Liquidity","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121691767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-01DOI: 10.1142/s2382626620500124
Bastien Baldacci, Philippe Bergault
With the fragmentation of electronic markets, exchanges are now competing in order to attract trading activity on their platform. Consequently, they developed several regulatory tools to control liquidity provision / consumption on their liquidity pool. In this paper, we study the problem of an exchange using incentives in order to increase market liquidity. We model the limit order book as the solution of a stochastic partial differential equation (SPDE) as in [12]. The incentives proposed to the market participants are functions of the time and the distance of their limit order to the mid-price. We formulate the control problem of the exchange who wishes to modify the shape of the order book by increasing the volume at specific limits. Due to the particular nature of the SPDE control problem, we are able to characterize the solution with a classic Feynman-Kac representation theorem. Moreover, when studying the asymptotic behavior of the solution, a specific penalty function enables the exchange to obtain closed-form incentives at each limit of the order book. We study numerically the form of the incentives and their impact on the shape of the order book, and analyze the sensitivity of the incentives to the market parameters.
{"title":"Optimal incentives in a limit order book: a SPDE control approach","authors":"Bastien Baldacci, Philippe Bergault","doi":"10.1142/s2382626620500124","DOIUrl":"https://doi.org/10.1142/s2382626620500124","url":null,"abstract":"With the fragmentation of electronic markets, exchanges are now competing in order to attract trading activity on their platform. Consequently, they developed several regulatory tools to control liquidity provision / consumption on their liquidity pool. In this paper, we study the problem of an exchange using incentives in order to increase market liquidity. We model the limit order book as the solution of a stochastic partial differential equation (SPDE) as in [12]. The incentives proposed to the market participants are functions of the time and the distance of their limit order to the mid-price. We formulate the control problem of the exchange who wishes to modify the shape of the order book by increasing the volume at specific limits. Due to the particular nature of the SPDE control problem, we are able to characterize the solution with a classic Feynman-Kac representation theorem. Moreover, when studying the asymptotic behavior of the solution, a specific penalty function enables the exchange to obtain closed-form incentives at each limit of the order book. We study numerically the form of the incentives and their impact on the shape of the order book, and analyze the sensitivity of the incentives to the market parameters.","PeriodicalId":232544,"journal":{"name":"Market Microstructure and Liquidity","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116426721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-27DOI: 10.1142/s2382626620500148
Emmanouil Sfendourakis, I. Toke
A point process model for order flows in limit order books is proposed, in which the conditional intensity is the product of a Hawkes component and a state-dependent factor. In the LOB context, state observations may include the observed imbalance or the observed spread. Full technical details for the computationally-efficient estimation of such a process are provided, using either direct likelihood maximization or EM-type estimation. Applications include models for bid and ask market orders, or for upwards and downwards price movements. Empirical results on multiple stocks traded in Euronext Paris underline the benefits of state-dependent formulations for LOB modeling, e.g. in terms of goodness-of-fit to financial data.
{"title":"LOB modeling using Hawkes processes with a state-dependent factor","authors":"Emmanouil Sfendourakis, I. Toke","doi":"10.1142/s2382626620500148","DOIUrl":"https://doi.org/10.1142/s2382626620500148","url":null,"abstract":"A point process model for order flows in limit order books is proposed, in which the conditional intensity is the product of a Hawkes component and a state-dependent factor. In the LOB context, state observations may include the observed imbalance or the observed spread. Full technical details for the computationally-efficient estimation of such a process are provided, using either direct likelihood maximization or EM-type estimation. Applications include models for bid and ask market orders, or for upwards and downwards price movements. Empirical results on multiple stocks traded in Euronext Paris underline the benefits of state-dependent formulations for LOB modeling, e.g. in terms of goodness-of-fit to financial data.","PeriodicalId":232544,"journal":{"name":"Market Microstructure and Liquidity","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123957069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-31DOI: 10.1142/s2382626620500100
Joffrey Derchu
We introduce a simple framework in which market participants update their prior about an efficient price with a model-based learning process. We show that exponential intensities for the arrival of aggressive orders arise naturally in this setting. Our approach allows us to fully describe market dynamics in the case with Brownian efficient price and informed market takers. We are also able to revisit the emergence of market impact due to meta-order splitting, making several connections with existing literature.
{"title":"A Bayesian viewpoint on the price formation process","authors":"Joffrey Derchu","doi":"10.1142/s2382626620500100","DOIUrl":"https://doi.org/10.1142/s2382626620500100","url":null,"abstract":"We introduce a simple framework in which market participants update their prior about an efficient price with a model-based learning process. We show that exponential intensities for the arrival of aggressive orders arise naturally in this setting. Our approach allows us to fully describe market dynamics in the case with Brownian efficient price and informed market takers. We are also able to revisit the emergence of market impact due to meta-order splitting, making several connections with existing literature.","PeriodicalId":232544,"journal":{"name":"Market Microstructure and Liquidity","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122752031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-07DOI: 10.1142/s2382626620500069
Benjamin M. Blau, Ryan J. Whitby
In this study, we examine the trading activity and volatility of stocks influenced by the U.S. Securities and Exchange Commission’s pilot program that increases tick sizes for various samples of stocks. The objective of the program is to improve the market quality of small-cap stocks, which have historically been relatively less liquid than other stocks. Using a difference-in-differences approach, we find that, relative to control stocks, the trading activity of pilot stocks does not appear to be meaningfully affected by the increase in tick sizes. Volatility, however, increases markedly for the pilot stocks compared to non-pilot stocks. These results are robust to the three different sets of pilot stocks, various rollout periods, and different control groups. We also find that pilot stocks tend to cluster on round increments of $0.05 more frequently than non-pilot stocks after the rollout periods. This is true particularly for pilot stocks that quote on $0.05 but trade on $0.01. To the extent that prices convey important information to market participants, these latter results suggest that the discreteness in prices imposed by the pilot program may adversely affect the informativeness of prices in equity markets.
{"title":"Rethinking Decimalization: The Impact of Increased Tick Sizes on Trading Activity, Volatility, and Price Clustering","authors":"Benjamin M. Blau, Ryan J. Whitby","doi":"10.1142/s2382626620500069","DOIUrl":"https://doi.org/10.1142/s2382626620500069","url":null,"abstract":"In this study, we examine the trading activity and volatility of stocks influenced by the U.S. Securities and Exchange Commission’s pilot program that increases tick sizes for various samples of stocks. The objective of the program is to improve the market quality of small-cap stocks, which have historically been relatively less liquid than other stocks. Using a difference-in-differences approach, we find that, relative to control stocks, the trading activity of pilot stocks does not appear to be meaningfully affected by the increase in tick sizes. Volatility, however, increases markedly for the pilot stocks compared to non-pilot stocks. These results are robust to the three different sets of pilot stocks, various rollout periods, and different control groups. We also find that pilot stocks tend to cluster on round increments of $0.05 more frequently than non-pilot stocks after the rollout periods. This is true particularly for pilot stocks that quote on $0.05 but trade on $0.01. To the extent that prices convey important information to market participants, these latter results suggest that the discreteness in prices imposed by the pilot program may adversely affect the informativeness of prices in equity markets.","PeriodicalId":232544,"journal":{"name":"Market Microstructure and Liquidity","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124709218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-18DOI: 10.1142/s2382626620500082
Bastien Baldacci, Iuliia Manziuk
In this article, we provide a flexible framework for optimal trading in an asset listed on different venues. We take into account the dependencies between the imbalance and spread of the venues, and allow for partial execution of limit orders at different limits as well as market orders. We present a Bayesian update of the model parameters to take into account possibly changing market conditions and propose extensions to include short/long trading signals, market impact or hidden liquidity. To solve the stochastic control problem of the trader we apply the finite difference method and also develop a deep reinforcement learning algorithm allowing to consider more complex settings.
{"title":"Adaptive trading strategies across liquidity pools","authors":"Bastien Baldacci, Iuliia Manziuk","doi":"10.1142/s2382626620500082","DOIUrl":"https://doi.org/10.1142/s2382626620500082","url":null,"abstract":"In this article, we provide a flexible framework for optimal trading in an asset listed on different venues. We take into account the dependencies between the imbalance and spread of the venues, and allow for partial execution of limit orders at different limits as well as market orders. We present a Bayesian update of the model parameters to take into account possibly changing market conditions and propose extensions to include short/long trading signals, market impact or hidden liquidity. To solve the stochastic control problem of the trader we apply the finite difference method and also develop a deep reinforcement learning algorithm allowing to consider more complex settings.","PeriodicalId":232544,"journal":{"name":"Market Microstructure and Liquidity","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130931670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-01DOI: 10.1142/s2382626619500102
Christoph Belak, Johannes Muhle‐Karbe, Kevin Ou
We study optimal liquidation in “target zone models” — asset prices with a reflecting boundary enforced by regulatory interventions. This can be treated as a special case of an Almgren–Chriss model with running and terminal inventory costs and general predictive signals about price changes. The optimal liquidation rate in target-zone models can in turn be characterized as the “theta” of a lookback option, leading to explicit formulas for Bachelier or Black–Scholes dynamics.
{"title":"Liquidation in Target Zone Models","authors":"Christoph Belak, Johannes Muhle‐Karbe, Kevin Ou","doi":"10.1142/s2382626619500102","DOIUrl":"https://doi.org/10.1142/s2382626619500102","url":null,"abstract":"We study optimal liquidation in “target zone models” — asset prices with a reflecting boundary enforced by regulatory interventions. This can be treated as a special case of an Almgren–Chriss model with running and terminal inventory costs and general predictive signals about price changes. The optimal liquidation rate in target-zone models can in turn be characterized as the “theta” of a lookback option, leading to explicit formulas for Bachelier or Black–Scholes dynamics.","PeriodicalId":232544,"journal":{"name":"Market Microstructure and Liquidity","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132577185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-01DOI: 10.1142/s2382626619500096
D. Gakhar, S. Kundlia
Main objective of the study is to analyze firm characteristics which affect stock illiquidity. The paper aims to give suggestions and policy implications to corporates and investors while dealing with investments in illiquid stocks. ANOVA, chi-square tests, correlation analysis, univariate and multiple regression models are employed on Amihud (2002) (Amihud, Y., (2002). Illiquidity and Stock Returns: Cross-Section and Time-Series Effects, Journal of Financial Markets 5, 31–56) illiquidity measure and various firm characteristics. Findings of this paper suggest that firms with illiquid stocks can be characterized with low promoter’s stakes, high leverage, poor financial health, small size and low/negative profitability. The findings of the paper will be of relevance to retail investors who are at the mercy of informed investors. The results portray basic characteristics that an investor should look into before investing in any stock. The study is of value to the investors who are grieved because of the adverse selections and information asymmetry. Moreover, the basic nature of illiquid firms has never been studied.
{"title":"Stock Illiquidity and Firm Characteristics","authors":"D. Gakhar, S. Kundlia","doi":"10.1142/s2382626619500096","DOIUrl":"https://doi.org/10.1142/s2382626619500096","url":null,"abstract":"Main objective of the study is to analyze firm characteristics which affect stock illiquidity. The paper aims to give suggestions and policy implications to corporates and investors while dealing with investments in illiquid stocks. ANOVA, chi-square tests, correlation analysis, univariate and multiple regression models are employed on Amihud (2002) (Amihud, Y., (2002). Illiquidity and Stock Returns: Cross-Section and Time-Series Effects, Journal of Financial Markets 5, 31–56) illiquidity measure and various firm characteristics. Findings of this paper suggest that firms with illiquid stocks can be characterized with low promoter’s stakes, high leverage, poor financial health, small size and low/negative profitability. The findings of the paper will be of relevance to retail investors who are at the mercy of informed investors. The results portray basic characteristics that an investor should look into before investing in any stock. The study is of value to the investors who are grieved because of the adverse selections and information asymmetry. Moreover, the basic nature of illiquid firms has never been studied.","PeriodicalId":232544,"journal":{"name":"Market Microstructure and Liquidity","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121617696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-10DOI: 10.1142/s238262662050001x
Xiangge Luo, A. Schied
We consider a market impact game for [Formula: see text] risk-averse agents that are competing in a market model with linear transient price impact and additional transaction costs. For both finite and infinite time horizons, the agents aim to minimize a mean-variance functional of their costs or to maximize the expected exponential utility of their revenues. We give explicit representations for corresponding Nash equilibria and prove uniqueness in the case of mean-variance optimization. A qualitative analysis of these Nash equilibria is conducted by means of numerical analysis.
{"title":"Nash Equilibrium for Risk-Averse Investors in a Market Impact Game with Transient Price Impact","authors":"Xiangge Luo, A. Schied","doi":"10.1142/s238262662050001x","DOIUrl":"https://doi.org/10.1142/s238262662050001x","url":null,"abstract":"We consider a market impact game for [Formula: see text] risk-averse agents that are competing in a market model with linear transient price impact and additional transaction costs. For both finite and infinite time horizons, the agents aim to minimize a mean-variance functional of their costs or to maximize the expected exponential utility of their revenues. We give explicit representations for corresponding Nash equilibria and prove uniqueness in the case of mean-variance optimization. A qualitative analysis of these Nash equilibria is conducted by means of numerical analysis.","PeriodicalId":232544,"journal":{"name":"Market Microstructure and Liquidity","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127871801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-02-16DOI: 10.1142/S2382626620500045
Ismael Lemhadri
The latent order book of [Donier et al., 2015, A fully consistent, minimal model for nonlinear market impact, Quantitative Finance 15(7), 1109–1121] is one of the most promising agent-based models for market impact. This work extends the minimal model by allowing agents to exhibit mean-reversion, a commonly observed pattern in real markets. This modification leads to new order book dynamics, which we explicitly study and analyze. Underlying our analysis is a mean-field assumption that views the order book through its average density. We show how price impact develops in this new model, providing a flexible family of solutions that can potentially be calibrated to real data. While no closed-form solution is provided, we complement our theoretical investigation with extensive numerical results, including a simulation scheme for the entire order book.
[Donier et al.， 2015, A fully consistent, minimum model for nonlinear market impact, Quantitative Finance 15(7)， 1109-1121]的latent order book是最有前途的基于agent的市场影响模型之一。这项工作扩展了最小模型，允许代理人表现出均值回归，这是真实市场中常见的模式。这种修改导致了新订单的动态变化，我们对此进行了明确的研究和分析。我们分析的基础是一个平均场假设，它通过平均密度来看待订单簿。我们展示了价格影响在这个新模型中是如何发展的，提供了一系列灵活的解决方案，可以根据实际数据进行校准。虽然没有提供封闭形式的解决方案，但我们用广泛的数值结果补充了我们的理论研究，包括整个订单的模拟方案。
{"title":"Price Impact in a Latent Order Book","authors":"Ismael Lemhadri","doi":"10.1142/S2382626620500045","DOIUrl":"https://doi.org/10.1142/S2382626620500045","url":null,"abstract":"The latent order book of [Donier et al., 2015, A fully consistent, minimal model for nonlinear market impact, Quantitative Finance 15(7), 1109–1121] is one of the most promising agent-based models for market impact. This work extends the minimal model by allowing agents to exhibit mean-reversion, a commonly observed pattern in real markets. This modification leads to new order book dynamics, which we explicitly study and analyze. Underlying our analysis is a mean-field assumption that views the order book through its average density. We show how price impact develops in this new model, providing a flexible family of solutions that can potentially be calibrated to real data. While no closed-form solution is provided, we complement our theoretical investigation with extensive numerical results, including a simulation scheme for the entire order book.","PeriodicalId":232544,"journal":{"name":"Market Microstructure and Liquidity","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125244387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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