Cecilia Aubrun, Rudy Morel, Michael Benzaquen, Jean-Philippe Bouchaud
Cascades of events and extreme occurrences have garnered significant attention across diverse domains such as financial markets, seismology, and social physics. Such events can stem either from the internal dynamics inherent to the system (endogenous), or from external shocks (exogenous). The possibility of separating these two classes of events has critical implications for professionals in those fields. We introduce an unsupervised framework leveraging a representation of jump time-series based on wavelet coefficients and apply it to stock price jumps. In line with previous work, we recover the fact that the time-asymmetry of volatility is a major feature. Mean-reversion and trend are found to be two additional key features, allowing us to identify new classes of jumps. Furthermore, thanks to our wavelet-based representation, we investigate the reflexive properties of co-jumps, which occur when multiple stocks experience price jumps within the same minute. We argue that a significant fraction of co-jumps results from an endogenous contagion mechanism.
{"title":"Riding Wavelets: A Method to Discover New Classes of Price Jumps","authors":"Cecilia Aubrun, Rudy Morel, Michael Benzaquen, Jean-Philippe Bouchaud","doi":"arxiv-2404.16467","DOIUrl":"https://doi.org/arxiv-2404.16467","url":null,"abstract":"Cascades of events and extreme occurrences have garnered significant\u0000attention across diverse domains such as financial markets, seismology, and\u0000social physics. Such events can stem either from the internal dynamics inherent\u0000to the system (endogenous), or from external shocks (exogenous). The\u0000possibility of separating these two classes of events has critical implications\u0000for professionals in those fields. We introduce an unsupervised framework\u0000leveraging a representation of jump time-series based on wavelet coefficients\u0000and apply it to stock price jumps. In line with previous work, we recover the\u0000fact that the time-asymmetry of volatility is a major feature. Mean-reversion\u0000and trend are found to be two additional key features, allowing us to identify\u0000new classes of jumps. Furthermore, thanks to our wavelet-based representation,\u0000we investigate the reflexive properties of co-jumps, which occur when multiple\u0000stocks experience price jumps within the same minute. We argue that a\u0000significant fraction of co-jumps results from an endogenous contagion\u0000mechanism.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805356","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}
Maximal Extractable Value (MEV) in Constant Function Market Making is fairly well understood. Does having dynamic weights, as found in liquidity boostrap pools (LBPs), Temporal-function market makers (TFMMs), and Replicating market makers (RMMs), introduce new attack vectors? In this paper we explore how inter-block weight changes can be analogous to trades, and can potentially lead to a multi-block MEV attack. New inter-block protections required to guard against this new attack vector are analysed. We also carry our a raft of numerical simulations, more than 450 million potential attack scenarios, showing both successful attacks and successful defense.
{"title":"Multiblock MEV opportunities & protections in dynamic AMMs","authors":"Matthew Willetts, Christian Harrington","doi":"arxiv-2404.15489","DOIUrl":"https://doi.org/arxiv-2404.15489","url":null,"abstract":"Maximal Extractable Value (MEV) in Constant Function Market Making is fairly\u0000well understood. Does having dynamic weights, as found in liquidity boostrap\u0000pools (LBPs), Temporal-function market makers (TFMMs), and Replicating market\u0000makers (RMMs), introduce new attack vectors? In this paper we explore how\u0000inter-block weight changes can be analogous to trades, and can potentially lead\u0000to a multi-block MEV attack. New inter-block protections required to guard\u0000against this new attack vector are analysed. We also carry our a raft of\u0000numerical simulations, more than 450 million potential attack scenarios,\u0000showing both successful attacks and successful defense.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":"101 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805187","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}
Alexander Barzykin, Philippe Bergault, Olivier Guéant
The primary challenge of market making in spot precious metals is navigating the liquidity that is mainly provided by futures contracts. The Exchange for Physical (EFP) spread, which is the price difference between futures and spot, plays a pivotal role and exhibits multiple modes of relaxation corresponding to the diverse trading horizons of market participants. In this paper, we introduce a novel framework utilizing a nested Ornstein-Uhlenbeck process to model the EFP spread. We demonstrate the suitability of the framework for maximizing the expected P&L of a market maker while minimizing inventory risk across both spot and futures. Using a computationally efficient technique to approximate the solution of the Hamilton-Jacobi-Bellman equation associated with the corresponding stochastic optimal control problem, our methodology facilitates strategy optimization on demand in near real-time, paving the way for advanced algorithmic market making that capitalizes on the co-integration properties intrinsic to the precious metals sector.
{"title":"Algorithmic Market Making in Spot Precious Metals","authors":"Alexander Barzykin, Philippe Bergault, Olivier Guéant","doi":"arxiv-2404.15478","DOIUrl":"https://doi.org/arxiv-2404.15478","url":null,"abstract":"The primary challenge of market making in spot precious metals is navigating\u0000the liquidity that is mainly provided by futures contracts. The Exchange for\u0000Physical (EFP) spread, which is the price difference between futures and spot,\u0000plays a pivotal role and exhibits multiple modes of relaxation corresponding to\u0000the diverse trading horizons of market participants. In this paper, we\u0000introduce a novel framework utilizing a nested Ornstein-Uhlenbeck process to\u0000model the EFP spread. We demonstrate the suitability of the framework for\u0000maximizing the expected P&L of a market maker while minimizing inventory risk\u0000across both spot and futures. Using a computationally efficient technique to\u0000approximate the solution of the Hamilton-Jacobi-Bellman equation associated\u0000with the corresponding stochastic optimal control problem, our methodology\u0000facilitates strategy optimization on demand in near real-time, paving the way\u0000for advanced algorithmic market making that capitalizes on the co-integration\u0000properties intrinsic to the precious metals sector.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805363","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}
Yifan He, Abootaleb Shirvani, Barret Shao, Svetlozar Rachev, Frank Fabozzi
This study introduces novel concepts in the analysis of limit order books (LOBs) with a focus on unveiling strategic insights into spread prediction and understanding the global mid-price (GMP) phenomenon. We define and analyze the total market order book bid--ask spread (TMOBBAS) and GMP, showcasing their significance in providing a deeper understanding of market dynamics beyond traditional LOB models. Employing high-frequency data, we comprehensively examine these concepts through various methodological lenses, including tail behavior analysis, dynamics of log-returns, and risk--return performance evaluation. Our findings reveal the intricate behavior of TMOBBAS and GMP under different market conditions, offering new perspectives on the liquidity, volatility, and efficiency of markets. This paper not only contributes to the academic discourse on financial markets but also presents practical implications for traders, risk managers, and policymakers seeking to navigate the complexities of modern financial systems.
{"title":"Beyond the Bid-Ask: Strategic Insights into Spread Prediction and the Global Mid-Price Phenomenon","authors":"Yifan He, Abootaleb Shirvani, Barret Shao, Svetlozar Rachev, Frank Fabozzi","doi":"arxiv-2404.11722","DOIUrl":"https://doi.org/arxiv-2404.11722","url":null,"abstract":"This study introduces novel concepts in the analysis of limit order books\u0000(LOBs) with a focus on unveiling strategic insights into spread prediction and\u0000understanding the global mid-price (GMP) phenomenon. We define and analyze the\u0000total market order book bid--ask spread (TMOBBAS) and GMP, showcasing their\u0000significance in providing a deeper understanding of market dynamics beyond\u0000traditional LOB models. Employing high-frequency data, we comprehensively\u0000examine these concepts through various methodological lenses, including tail\u0000behavior analysis, dynamics of log-returns, and risk--return performance\u0000evaluation. Our findings reveal the intricate behavior of TMOBBAS and GMP under\u0000different market conditions, offering new perspectives on the liquidity,\u0000volatility, and efficiency of markets. This paper not only contributes to the\u0000academic discourse on financial markets but also presents practical\u0000implications for traders, risk managers, and policymakers seeking to navigate\u0000the complexities of modern financial systems.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140629903","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 investigate the behavior of liquidity providers (LPs) by modeling a decentralized cryptocurrency exchange (DEX) based on Uniswap v3. LPs with heterogeneous characteristics choose optimal liquidity positions subject to uncertainty regarding the size of exogenous incoming transactions and the prices of assets in the wider market. They engage in a game among themselves, and the resulting liquidity distribution determines the exchange rate dynamics and potential arbitrage opportunities of the pool. We calibrate the distribution of LP characteristics based on Uniswap data and the equilibrium strategy resulting from this mean-field game produces pool exchange rate dynamics and liquidity evolution consistent with observed pool behavior. We subsequently introduce Maximal Extractable Value (MEV) bots who perform Just-In-Time (JIT) liquidity attacks, and develop a Stackelberg game between LPs and bots. This addition results in more accurate simulated pool exchange rate dynamics and stronger predictive power regarding the evolution of the pool liquidity distribution.
{"title":"DEX Specs: A Mean Field Approach to DeFi Currency Exchanges","authors":"Erhan Bayraktar, Asaf Cohen, April Nellis","doi":"arxiv-2404.09090","DOIUrl":"https://doi.org/arxiv-2404.09090","url":null,"abstract":"We investigate the behavior of liquidity providers (LPs) by modeling a\u0000decentralized cryptocurrency exchange (DEX) based on Uniswap v3. LPs with\u0000heterogeneous characteristics choose optimal liquidity positions subject to\u0000uncertainty regarding the size of exogenous incoming transactions and the\u0000prices of assets in the wider market. They engage in a game among themselves,\u0000and the resulting liquidity distribution determines the exchange rate dynamics\u0000and potential arbitrage opportunities of the pool. We calibrate the\u0000distribution of LP characteristics based on Uniswap data and the equilibrium\u0000strategy resulting from this mean-field game produces pool exchange rate\u0000dynamics and liquidity evolution consistent with observed pool behavior. We\u0000subsequently introduce Maximal Extractable Value (MEV) bots who perform\u0000Just-In-Time (JIT) liquidity attacks, and develop a Stackelberg game between\u0000LPs and bots. This addition results in more accurate simulated pool exchange\u0000rate dynamics and stronger predictive power regarding the evolution of the pool\u0000liquidity distribution.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570280","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}
This paper presents the results of a comprehensive empirical study of losses to arbitrageurs (following the formalization of loss-versus-rebalancing by [Milionis et al., 2022]) incurred by liquidity on automated market makers (AMMs). Through a systematic comparison between historical earnings from trading fees and losses to arbitrageurs, our findings indicate an insufficient compensation from fees for arbitrage losses across many of the largest AMM liquidity pools (on Uniswap). Remarkably, we identify a higher profitability among less capital-efficient Uniswap v2 pools compared to their Uniswap v3 counterparts. Moreover, we investigate a possible LVR mitigation by quantifying how arbitrage losses reduce with shorter block times. We observe notable variations in the manner of decline of arbitrage losses across different trading pairs. For instance, when comparing 100ms block times to Ethereum's current 12-second block times, the decrease in losses to arbitrageurs ranges between 20% to 70%, depending on the specific trading pair.
{"title":"Measuring Arbitrage Losses and Profitability of AMM Liquidity","authors":"Robin Fritsch, Andrea Canidio","doi":"arxiv-2404.05803","DOIUrl":"https://doi.org/arxiv-2404.05803","url":null,"abstract":"This paper presents the results of a comprehensive empirical study of losses\u0000to arbitrageurs (following the formalization of loss-versus-rebalancing by\u0000[Milionis et al., 2022]) incurred by liquidity on automated market makers\u0000(AMMs). Through a systematic comparison between historical earnings from\u0000trading fees and losses to arbitrageurs, our findings indicate an insufficient\u0000compensation from fees for arbitrage losses across many of the largest AMM\u0000liquidity pools (on Uniswap). Remarkably, we identify a higher profitability\u0000among less capital-efficient Uniswap v2 pools compared to their Uniswap v3\u0000counterparts. Moreover, we investigate a possible LVR mitigation by quantifying\u0000how arbitrage losses reduce with shorter block times. We observe notable\u0000variations in the manner of decline of arbitrage losses across different\u0000trading pairs. For instance, when comparing 100ms block times to Ethereum's\u0000current 12-second block times, the decrease in losses to arbitrageurs ranges\u0000between 20% to 70%, depending on the specific trading pair.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570282","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}
This paper investigates the enhancement of financial time series forecasting with the use of neural networks through supervised autoencoders, aiming to improve investment strategy performance. It specifically examines the impact of noise augmentation and triple barrier labeling on risk-adjusted returns, using the Sharpe and Information Ratios. The study focuses on the S&P 500 index, EUR/USD, and BTC/USD as the traded assets from January 1, 2010, to April 30, 2022. Findings indicate that supervised autoencoders, with balanced noise augmentation and bottleneck size, significantly boost strategy effectiveness. However, excessive noise and large bottleneck sizes can impair performance, highlighting the importance of precise parameter tuning. This paper also presents a derivation of a novel optimization metric that can be used with triple barrier labeling. The results of this study have substantial policy implications, suggesting that financial institutions and regulators could leverage techniques presented to enhance market stability and investor protection, while also encouraging more informed and strategic investment approaches in various financial sectors.
{"title":"Supervised Autoencoder MLP for Financial Time Series Forecasting","authors":"Bartosz Bieganowski, Robert Slepaczuk","doi":"arxiv-2404.01866","DOIUrl":"https://doi.org/arxiv-2404.01866","url":null,"abstract":"This paper investigates the enhancement of financial time series forecasting\u0000with the use of neural networks through supervised autoencoders, aiming to\u0000improve investment strategy performance. It specifically examines the impact of\u0000noise augmentation and triple barrier labeling on risk-adjusted returns, using\u0000the Sharpe and Information Ratios. The study focuses on the S&P 500 index,\u0000EUR/USD, and BTC/USD as the traded assets from January 1, 2010, to April 30,\u00002022. Findings indicate that supervised autoencoders, with balanced noise\u0000augmentation and bottleneck size, significantly boost strategy effectiveness.\u0000However, excessive noise and large bottleneck sizes can impair performance,\u0000highlighting the importance of precise parameter tuning. This paper also\u0000presents a derivation of a novel optimization metric that can be used with\u0000triple barrier labeling. The results of this study have substantial policy\u0000implications, suggesting that financial institutions and regulators could\u0000leverage techniques presented to enhance market stability and investor\u0000protection, while also encouraging more informed and strategic investment\u0000approaches in various financial sectors.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":"205 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570233","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}
Silvia García-Méndez, Francisco de Arriba-Pérez, Ana Barros-Vila, Francisco J. González-Castaño
Microblogging platforms, of which Twitter is a representative example, are valuable information sources for market screening and financial models. In them, users voluntarily provide relevant information, including educated knowledge on investments, reacting to the state of the stock markets in real-time and, often, influencing this state. We are interested in the user forecasts in financial, social media messages expressing opportunities and precautions about assets. We propose a novel Targeted Aspect-Based Emotion Analysis (TABEA) system that can individually discern the financial emotions (positive and negative forecasts) on the different stock market assets in the same tweet (instead of making an overall guess about that whole tweet). It is based on Natural Language Processing (NLP) techniques and Machine Learning streaming algorithms. The system comprises a constituency parsing module for parsing the tweets and splitting them into simpler declarative clauses; an offline data processing module to engineer textual, numerical and categorical features and analyse and select them based on their relevance; and a stream classification module to continuously process tweets on-the-fly. Experimental results on a labelled data set endorse our solution. It achieves over 90% precision for the target emotions, financial opportunity, and precaution on Twitter. To the best of our knowledge, no prior work in the literature has addressed this problem despite its practical interest in decision-making, and we are not aware of any previous NLP nor online Machine Learning approaches to TABEA.
{"title":"Targeted aspect-based emotion analysis to detect opportunities and precaution in financial Twitter messages","authors":"Silvia García-Méndez, Francisco de Arriba-Pérez, Ana Barros-Vila, Francisco J. González-Castaño","doi":"arxiv-2404.08665","DOIUrl":"https://doi.org/arxiv-2404.08665","url":null,"abstract":"Microblogging platforms, of which Twitter is a representative example, are\u0000valuable information sources for market screening and financial models. In\u0000them, users voluntarily provide relevant information, including educated\u0000knowledge on investments, reacting to the state of the stock markets in\u0000real-time and, often, influencing this state. We are interested in the user\u0000forecasts in financial, social media messages expressing opportunities and\u0000precautions about assets. We propose a novel Targeted Aspect-Based Emotion\u0000Analysis (TABEA) system that can individually discern the financial emotions\u0000(positive and negative forecasts) on the different stock market assets in the\u0000same tweet (instead of making an overall guess about that whole tweet). It is\u0000based on Natural Language Processing (NLP) techniques and Machine Learning\u0000streaming algorithms. The system comprises a constituency parsing module for\u0000parsing the tweets and splitting them into simpler declarative clauses; an\u0000offline data processing module to engineer textual, numerical and categorical\u0000features and analyse and select them based on their relevance; and a stream\u0000classification module to continuously process tweets on-the-fly. Experimental\u0000results on a labelled data set endorse our solution. It achieves over 90%\u0000precision for the target emotions, financial opportunity, and precaution on\u0000Twitter. To the best of our knowledge, no prior work in the literature has\u0000addressed this problem despite its practical interest in decision-making, and\u0000we are not aware of any previous NLP nor online Machine Learning approaches to\u0000TABEA.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569990","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}
Zhiyuan Yao, Zheng Li, Matthew Thomas, Ionut Florescu
Investors and regulators can greatly benefit from a realistic market simulator that enables them to anticipate the consequences of their decisions in real markets. However, traditional rule-based market simulators often fall short in accurately capturing the dynamic behavior of market participants, particularly in response to external market impact events or changes in the behavior of other participants. In this study, we explore an agent-based simulation framework employing reinforcement learning (RL) agents. We present the implementation details of these RL agents and demonstrate that the simulated market exhibits realistic stylized facts observed in real-world markets. Furthermore, we investigate the behavior of RL agents when confronted with external market impacts, such as a flash crash. Our findings shed light on the effectiveness and adaptability of RL-based agents within the simulation, offering insights into their response to significant market events.
{"title":"Reinforcement Learning in Agent-Based Market Simulation: Unveiling Realistic Stylized Facts and Behavior","authors":"Zhiyuan Yao, Zheng Li, Matthew Thomas, Ionut Florescu","doi":"arxiv-2403.19781","DOIUrl":"https://doi.org/arxiv-2403.19781","url":null,"abstract":"Investors and regulators can greatly benefit from a realistic market\u0000simulator that enables them to anticipate the consequences of their decisions\u0000in real markets. However, traditional rule-based market simulators often fall\u0000short in accurately capturing the dynamic behavior of market participants,\u0000particularly in response to external market impact events or changes in the\u0000behavior of other participants. In this study, we explore an agent-based\u0000simulation framework employing reinforcement learning (RL) agents. We present\u0000the implementation details of these RL agents and demonstrate that the\u0000simulated market exhibits realistic stylized facts observed in real-world\u0000markets. Furthermore, we investigate the behavior of RL agents when confronted\u0000with external market impacts, such as a flash crash. Our findings shed light on\u0000the effectiveness and adaptability of RL-based agents within the simulation,\u0000offering insights into their response to significant market events.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":"123 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570338","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}
Geometric mean market makers (G3Ms), such as Uniswap and Balancer, represent a widely used class of automated market makers (AMMs). These G3Ms are characterized by the following rule: the reserves of the AMM must maintain the same (weighted) geometric mean before and after each trade. This paper investigates the effects of trading fees on liquidity providers' (LP) profitability in a G3M, as well as the adverse selection faced by LPs due to arbitrage activities involving a reference market. Our work expands the model described in previous studies for G3Ms, integrating transaction fees and continuous-time arbitrage into the analysis. Within this context, we analyze G3M dynamics, characterized by stochastic storage processes, and calculate the growth rate of LP wealth. In particular, our results align with and extend the results concerning the constant product market maker, commonly referred to as Uniswap v2.
{"title":"Growth rate of liquidity provider's wealth in G3Ms","authors":"Cheuk Yin Lee, Shen-Ning Tung, Tai-Ho Wang","doi":"arxiv-2403.18177","DOIUrl":"https://doi.org/arxiv-2403.18177","url":null,"abstract":"Geometric mean market makers (G3Ms), such as Uniswap and Balancer, represent\u0000a widely used class of automated market makers (AMMs). These G3Ms are\u0000characterized by the following rule: the reserves of the AMM must maintain the\u0000same (weighted) geometric mean before and after each trade. This paper\u0000investigates the effects of trading fees on liquidity providers' (LP)\u0000profitability in a G3M, as well as the adverse selection faced by LPs due to\u0000arbitrage activities involving a reference market. Our work expands the model\u0000described in previous studies for G3Ms, integrating transaction fees and\u0000continuous-time arbitrage into the analysis. Within this context, we analyze\u0000G3M dynamics, characterized by stochastic storage processes, and calculate the\u0000growth rate of LP wealth. In particular, our results align with and extend the\u0000results concerning the constant product market maker, commonly referred to as\u0000Uniswap v2.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311687","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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