Pub Date : 2016-09-02DOI: 10.1142/S2382626618500077
E. Strehle
Trading algorithms that execute large orders are susceptible to exploitation by order anticipation strategies. This paper studies the influence of order anticipation strategies in a multi-investor model of optimal execution under transient price impact. Existence and uniqueness of a Nash equilibrium is established under the assumption that trading incurs quadratic transaction costs. A closed-form representation of the Nash equilibrium is derived for exponential decay kernels. With this representation, it is shown that while order anticipation strategies raise the execution costs of a large order significantly, they typically do not cause price overshooting in the sense of Brunnermeier and Pedersen.
{"title":"Optimal Execution in a Multiplayer Model of Transient Price Impact","authors":"E. Strehle","doi":"10.1142/S2382626618500077","DOIUrl":"https://doi.org/10.1142/S2382626618500077","url":null,"abstract":"Trading algorithms that execute large orders are susceptible to exploitation by order anticipation strategies. This paper studies the influence of order anticipation strategies in a multi-investor model of optimal execution under transient price impact. Existence and uniqueness of a Nash equilibrium is established under the assumption that trading incurs quadratic transaction costs. A closed-form representation of the Nash equilibrium is derived for exponential decay kernels. With this representation, it is shown that while order anticipation strategies raise the execution costs of a large order significantly, they typically do not cause price overshooting in the sense of Brunnermeier and Pedersen.","PeriodicalId":8509,"journal":{"name":"arXiv: Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91143085","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 : 2016-04-10DOI: 10.1142/S2382626616500076
I. Toke
In this work we investigate tick-by-tick data provided by the TRTH database for several stocks on three different exchanges (Paris - Euronext, London and Frankfurt - Deutsche B"orse) and on a 5-year span. We use a simple algorithm that helps the synchronization of the trades and quotes data sources, providing enhancements to the basic procedure that, depending on the time period and the exchange, are shown to be significant. We show that the analysis of the performance of this algorithm turns out to be a a forensic tool assessing the quality of the aggregated database: we are able to track through the data some significant technical changes that occurred on the studied exchanges. We also illustrate the fact that the choices made when reconstructing order flows have consequences on the quantitative models that are calibrated afterwards on such data. Our study also provides elements on the trade signature, and we are able to give a more refined look at the standard Lee-Ready procedure, giving new elements on the way optimal lags should be chosen when using this method. The findings are in line with both financial reasoning and the analysis of an illustrative Poisson model of the order flow.
{"title":"Reconstruction of Order Flows using Aggregated Data","authors":"I. Toke","doi":"10.1142/S2382626616500076","DOIUrl":"https://doi.org/10.1142/S2382626616500076","url":null,"abstract":"In this work we investigate tick-by-tick data provided by the TRTH database for several stocks on three different exchanges (Paris - Euronext, London and Frankfurt - Deutsche B\"orse) and on a 5-year span. We use a simple algorithm that helps the synchronization of the trades and quotes data sources, providing enhancements to the basic procedure that, depending on the time period and the exchange, are shown to be significant. We show that the analysis of the performance of this algorithm turns out to be a a forensic tool assessing the quality of the aggregated database: we are able to track through the data some significant technical changes that occurred on the studied exchanges. We also illustrate the fact that the choices made when reconstructing order flows have consequences on the quantitative models that are calibrated afterwards on such data. Our study also provides elements on the trade signature, and we are able to give a more refined look at the standard Lee-Ready procedure, giving new elements on the way optimal lags should be chosen when using this method. The findings are in line with both financial reasoning and the analysis of an illustrative Poisson model of the order flow.","PeriodicalId":8509,"journal":{"name":"arXiv: Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82541795","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}
Fast trading and fragmentation of volume make equity markets complex, leading retail and institutional investors to demand sophisticated brokerage services. In a sample of stock transactions in Swedish large-cap firms, we find that brokers who show high trading sophistication when trading their own book do not deliver comparable execution quality when trading on behalf of clients. Best execution legislation states that brokers should take all reasonable steps to maximize the execution quality when trading on behalf of clients. For institutional clients, the shortcoming in execution quality is primarily driven by brokers' inability to route the transactions to the trading venue with the best price. For retail clients, in contrast, the shortcoming is due to poor liquidity timing and a strong reliance on active executions. Only institutional block trades benefit from execution by sophisticated brokers.
{"title":"Best Execution: Can Institutional and Retail Investors Benefit from Fast and Fragmented Trading?","authors":"Michał Dzieliński, Björn Hagströmer, Lars Norden","doi":"10.2139/ssrn.2719520","DOIUrl":"https://doi.org/10.2139/ssrn.2719520","url":null,"abstract":"Fast trading and fragmentation of volume make equity markets complex, leading retail and institutional investors to demand sophisticated brokerage services. In a sample of stock transactions in Swedish large-cap firms, we find that brokers who show high trading sophistication when trading their own book do not deliver comparable execution quality when trading on behalf of clients. Best execution legislation states that brokers should take all reasonable steps to maximize the execution quality when trading on behalf of clients. For institutional clients, the shortcoming in execution quality is primarily driven by brokers' inability to route the transactions to the trading venue with the best price. For retail clients, in contrast, the shortcoming is due to poor liquidity timing and a strong reliance on active executions. Only institutional block trades benefit from execution by sophisticated brokers.","PeriodicalId":8509,"journal":{"name":"arXiv: Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85240830","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}
We design and test neural networks for modeling the dynamics of the limit order book. In addition to testing traditional neural networks originally designed for classification, we develop a new neural network architecture for modeling spatial distributions (i.e., distributions on $mathbb{R}^d$) which takes advantage of local spatial structure. Model performance is tested on 140 S&P 500 and NASDAQ-100 stocks. The neural networks are trained using information from deep into the limit order book (i.e., many levels beyond the best bid and best ask). Techniques from deep learning such as dropout are employed to improve performance. Due to the computational challenges associated with the large amount of data, the neural networks are trained using GPU parallel computing. The neural networks are shown to outperform simpler models such as the naive empirical model and logistic regression, and the new neural network for spatial distributions outperforms the standard neural network.
{"title":"Extended Abstract: Neural Networks for Limit Order Books","authors":"Justin A. Sirignano","doi":"10.2139/ssrn.2710331","DOIUrl":"https://doi.org/10.2139/ssrn.2710331","url":null,"abstract":"We design and test neural networks for modeling the dynamics of the limit order book. In addition to testing traditional neural networks originally designed for classification, we develop a new neural network architecture for modeling spatial distributions (i.e., distributions on $mathbb{R}^d$) which takes advantage of local spatial structure. Model performance is tested on 140 S&P 500 and NASDAQ-100 stocks. The neural networks are trained using information from deep into the limit order book (i.e., many levels beyond the best bid and best ask). Techniques from deep learning such as dropout are employed to improve performance. Due to the computational challenges associated with the large amount of data, the neural networks are trained using GPU parallel computing. The neural networks are shown to outperform simpler models such as the naive empirical model and logistic regression, and the new neural network for spatial distributions outperforms the standard neural network.","PeriodicalId":8509,"journal":{"name":"arXiv: Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86358132","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}
We consider the role of special orders in informed traders' order submission strategies and their effect on the market price discovery process. Special orders, such as Fill-and-Kill and All-or-Nothing orders, are not entered in the order book; instead, they are executed immediately. This means they do not require costly monitoring and are not visible to other traders. Due to the fact that informed institutional traders, including high-frequency traders, use aggressive special orders, they generate higher price impacts than normal orders, particularly in volatile markets.
{"title":"The Information Content of Special Orders","authors":"H. N. Duong, P. Lajbcygier, V. Vu","doi":"10.2139/ssrn.2724847","DOIUrl":"https://doi.org/10.2139/ssrn.2724847","url":null,"abstract":"We consider the role of special orders in informed traders' order submission strategies and their effect on the market price discovery process. Special orders, such as Fill-and-Kill and All-or-Nothing orders, are not entered in the order book; instead, they are executed immediately. This means they do not require costly monitoring and are not visible to other traders. Due to the fact that informed institutional traders, including high-frequency traders, use aggressive special orders, they generate higher price impacts than normal orders, particularly in volatile markets.","PeriodicalId":8509,"journal":{"name":"arXiv: Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89445254","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 : 2015-02-01DOI: 10.1142/S021902491750039X
I. Toke
In this paper, we develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new value, either by a new limit order submitted inside the spread or by a market order that removes the first limit. Using applied probability results on killing and resurrecting Markov processes, we derive the stationary distribution of the volume offered at the best quote. All proposed models are empirically fitted and compared, stressing the importance of the proposed mechanisms.
{"title":"Stationary distribution of the volume at the best quote in a Poisson order book model","authors":"I. Toke","doi":"10.1142/S021902491750039X","DOIUrl":"https://doi.org/10.1142/S021902491750039X","url":null,"abstract":"In this paper, we develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new value, either by a new limit order submitted inside the spread or by a market order that removes the first limit. Using applied probability results on killing and resurrecting Markov processes, we derive the stationary distribution of the volume offered at the best quote. All proposed models are empirically fitted and compared, stressing the importance of the proposed mechanisms.","PeriodicalId":8509,"journal":{"name":"arXiv: Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84298416","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}
We study the problem of optimal trading using general alpha predictors with linear costs and temporary impact. We do this within the framework of stochastic optimization with finite horizon using both limit and market orders. Consistently with other studies, we find that the presence of linear costs induces a no-trading zone when using market orders, and a corresponding market-making zone when using limit orders. We show that, when combining both market and limit orders, the problem is further divided into zones in which we trade more aggressively using market orders. Even though we do not solve analytically the full optimization problem, we present explicit and simple analytical recipes which approximate the full solution and are easy to implement in practice. We test the algorithms using Monte Carlo simulations and show how they improve our Profit and Losses.
{"title":"Optimal Trading with Alpha Predictors","authors":"Filippo Passerini, Samuel E. Vázquez","doi":"10.21314/jois.2016.070","DOIUrl":"https://doi.org/10.21314/jois.2016.070","url":null,"abstract":"We study the problem of optimal trading using general alpha predictors with linear costs and temporary impact. We do this within the framework of stochastic optimization with finite horizon using both limit and market orders. Consistently with other studies, we find that the presence of linear costs induces a no-trading zone when using market orders, and a corresponding market-making zone when using limit orders. We show that, when combining both market and limit orders, the problem is further divided into zones in which we trade more aggressively using market orders. Even though we do not solve analytically the full optimization problem, we present explicit and simple analytical recipes which approximate the full solution and are easy to implement in practice. We test the algorithms using Monte Carlo simulations and show how they improve our Profit and Losses.","PeriodicalId":8509,"journal":{"name":"arXiv: Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80965540","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 : 2013-11-17DOI: 10.1007/978-3-319-09946-0_13
B. Myers, Austin Gerig
{"title":"Simulating the Synchronizing Behavior of High-Frequency Trading in Multiple Markets","authors":"B. Myers, Austin Gerig","doi":"10.1007/978-3-319-09946-0_13","DOIUrl":"https://doi.org/10.1007/978-3-319-09946-0_13","url":null,"abstract":"","PeriodicalId":8509,"journal":{"name":"arXiv: Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75477779","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}
Building on observations by Sch"oneborn (2008), we consider a Nash equilibrium between two high-frequency traders in a simple market impact model with transient price impact and additional quadratic transaction costs. We show that for small transaction costs the high-frequency traders engage in a "hot-potato game", in which the same asset position is sold back and forth. We then identify a critical value for the size of the transaction costs above which all oscillations disappear and strategies become buy-only or sell-only. Numerical simulations show that for both traders the expected costs can be lower with transaction costs than without. Moreover, the costs can increase with the trading frequency when there are no transaction costs, but decrease with the trading frequency when transaction costs are sufficiently high. We argue that these effects occur due to the need of protection against predatory trading in the regime of low transaction costs.
{"title":"A hot-potato game under transient price impact and some effects of a transaction tax","authors":"A. Schied, Zhang Tao","doi":"10.2139/ssrn.2256510","DOIUrl":"https://doi.org/10.2139/ssrn.2256510","url":null,"abstract":"Building on observations by Sch\"oneborn (2008), we consider a Nash equilibrium between two high-frequency traders in a simple market impact model with transient price impact and additional quadratic transaction costs. We show that for small transaction costs the high-frequency traders engage in a \"hot-potato game\", in which the same asset position is sold back and forth. We then identify a critical value for the size of the transaction costs above which all oscillations disappear and strategies become buy-only or sell-only. Numerical simulations show that for both traders the expected costs can be lower with transaction costs than without. Moreover, the costs can increase with the trading frequency when there are no transaction costs, but decrease with the trading frequency when transaction costs are sufficiently high. We argue that these effects occur due to the need of protection against predatory trading in the regime of low transaction costs.","PeriodicalId":8509,"journal":{"name":"arXiv: Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79351077","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 : 2013-02-19DOI: 10.1017/CBO9781139151184.029
Charles-Albert Lehalle
A great deal of academic and theoretical work has been dedicated to optimal liquidation of large orders these last twenty years. The optimal split of an order through time (`optimal trade scheduling') and space (`smart order routing') is of high interest rred{to} practitioners because of the increasing complexity of the market micro structure because of the evolution recently of regulations and liquidity worldwide. This paper translates into quantitative terms these regulatory issues and, more broadly, current market design. It relates the recent advances in optimal trading, order-book simulation and optimal liquidity to the reality of trading in an emerging global network of liquidity.
{"title":"Market Microstructure Knowledge Needed for Controlling an Intra-Day Trading Process","authors":"Charles-Albert Lehalle","doi":"10.1017/CBO9781139151184.029","DOIUrl":"https://doi.org/10.1017/CBO9781139151184.029","url":null,"abstract":"A great deal of academic and theoretical work has been dedicated to optimal liquidation of large orders these last twenty years. The optimal split of an order through time (`optimal trade scheduling') and space (`smart order routing') is of high interest rred{to} practitioners because of the increasing complexity of the market micro structure because of the evolution recently of regulations and liquidity worldwide. This paper translates into quantitative terms these regulatory issues and, more broadly, current market design. It relates the recent advances in optimal trading, order-book simulation and optimal liquidity to the reality of trading in an emerging global network of liquidity.","PeriodicalId":8509,"journal":{"name":"arXiv: Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83447484","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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