{"title":"市场影响的贝叶斯理论","authors":"Louis Saddier, Matteo Marsili","doi":"10.1088/1742-5468/ad5271","DOIUrl":null,"url":null,"abstract":"The available liquidity at any time in financial markets falls largely short of the typical size of the orders that institutional investors would trade. In order to reduce the impact on prices due to the execution of large orders, traders in financial markets split large orders into a series of smaller ones, which are executed sequentially. The resulting sequence of trades is called a meta-order. Empirical studies have revealed a non-trivial set of statistical laws on how meta-orders affect prices, which include (i) the square-root behaviour of the expected price variation with the total volume traded, (ii) its crossover to a linear regime for small volumes and (iii) a reversion of average prices towards its initial value, after the sequence of trades is over. Here we recover this phenomenology within a minimal theoretical framework where the market sets prices by incorporating all information on the direction and speed of trade of the meta-order in a Bayesian manner. The simplicity of this derivation lends further support to the robustness and universality of market impact laws. In particular, it suggests that the square-root impact law originates from over-estimation of order flows originating from meta-orders.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Bayesian theory of market impact\",\"authors\":\"Louis Saddier, Matteo Marsili\",\"doi\":\"10.1088/1742-5468/ad5271\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The available liquidity at any time in financial markets falls largely short of the typical size of the orders that institutional investors would trade. In order to reduce the impact on prices due to the execution of large orders, traders in financial markets split large orders into a series of smaller ones, which are executed sequentially. The resulting sequence of trades is called a meta-order. Empirical studies have revealed a non-trivial set of statistical laws on how meta-orders affect prices, which include (i) the square-root behaviour of the expected price variation with the total volume traded, (ii) its crossover to a linear regime for small volumes and (iii) a reversion of average prices towards its initial value, after the sequence of trades is over. Here we recover this phenomenology within a minimal theoretical framework where the market sets prices by incorporating all information on the direction and speed of trade of the meta-order in a Bayesian manner. The simplicity of this derivation lends further support to the robustness and universality of market impact laws. In particular, it suggests that the square-root impact law originates from over-estimation of order flows originating from meta-orders.\",\"PeriodicalId\":17207,\"journal\":{\"name\":\"Journal of Statistical Mechanics: Theory and Experiment\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Statistical Mechanics: Theory and Experiment\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1742-5468/ad5271\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Mechanics: Theory and Experiment","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1742-5468/ad5271","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
The available liquidity at any time in financial markets falls largely short of the typical size of the orders that institutional investors would trade. In order to reduce the impact on prices due to the execution of large orders, traders in financial markets split large orders into a series of smaller ones, which are executed sequentially. The resulting sequence of trades is called a meta-order. Empirical studies have revealed a non-trivial set of statistical laws on how meta-orders affect prices, which include (i) the square-root behaviour of the expected price variation with the total volume traded, (ii) its crossover to a linear regime for small volumes and (iii) a reversion of average prices towards its initial value, after the sequence of trades is over. Here we recover this phenomenology within a minimal theoretical framework where the market sets prices by incorporating all information on the direction and speed of trade of the meta-order in a Bayesian manner. The simplicity of this derivation lends further support to the robustness and universality of market impact laws. In particular, it suggests that the square-root impact law originates from over-estimation of order flows originating from meta-orders.
期刊介绍:
JSTAT is targeted to a broad community interested in different aspects of statistical physics, which are roughly defined by the fields represented in the conferences called ''Statistical Physics''. Submissions from experimentalists working on all the topics which have some ''connection to statistical physics are also strongly encouraged.
The journal covers different topics which correspond to the following keyword sections.
1. Quantum statistical physics, condensed matter, integrable systems
Scientific Directors: Eduardo Fradkin and Giuseppe Mussardo
2. Classical statistical mechanics, equilibrium and non-equilibrium
Scientific Directors: David Mukamel, Matteo Marsili and Giuseppe Mussardo
3. Disordered systems, classical and quantum
Scientific Directors: Eduardo Fradkin and Riccardo Zecchina
4. Interdisciplinary statistical mechanics
Scientific Directors: Matteo Marsili and Riccardo Zecchina
5. Biological modelling and information
Scientific Directors: Matteo Marsili, William Bialek and Riccardo Zecchina