
 
 
 Umbhali: 
 
 
 
 U-Alvaro Cartea Fayc¸al Drissia Marcello Monga Authors: 
 
 
 
 U-Alvaro Cartea Izithombe ze-Al Drissia U-Marcello Monga Table Of Links Umbala we-Links abstract 1. Introduction I-Introduction 2. Constant function markets and concentrated liquidity 2. Izimakethe zokusebenza okuqhubekayo kanye ne-liquidity ehlanganisiwe 
 
 
 Izimakethe zokusebenza ngokuqinile I-Centralized Liquidity Market 3. The wealth of liquidity providers in CL pools I-Wealth of Liquidity Providers e-CL Pools 
 
 
 
 Imininingwane Fee income
 
 
 
 
 
 Fee income: pool fee rate Fee income: spread and concentration risk Fee income: drift and asymmetry I-re-balancing cost and gas fees 4. Optimal liquidity provision in CL pools I-Optimal Liquidity Provision ku-CL Pools 
 
 
 
 
 Ukuphendula Ukusebenza kwe-Optimal Strategy Ukubuyekezwa: Profitability, PL, ne-concentration risk Ukubuyekezwa: Drift and Position Skwow 5. Performance of strategy 5. Ukusebenza kweStrategy 
 
 
 
 Ukucaciswa Benchmark Imiphumela 6. Discussion: modelling assumptions I-Discussion: Ukuhlolwa kwama-assumptions 
 
 Ukubuyekezwa: Ukubuyekezwa 7. Conclusions And References I-Conclusions and References Abstract abstract I-Constant Product Markets with Concentrated Liquidity (CL) kuyinto uhlobo elidumile ye-Automated Market Makers. Kulesi sihloko, sincoma i-continuous-time wealth dynamics of strategic LPs that dynamically adjust their range of liquidity provision in CL pools. I-Wealth of them results from fee income, the value of their holdings in the pool, and rebalancing costs. Okulandelayo, sinikeza i-self-financing ne-closed-form optimum liquidity provision strategy lapho ububanzi we-liquidity range ye-LP ikakhulukazi yi-profitability ye-pool (izindleko ze-provision ekunciphiseni izindleko ze-gas), i-PL (i-PL) ye-position ye-LP, ne-concentration risk. I-concentration risk ibheka ukunciphisa ama-fee income uma i-limit exchange rate (e-accounted to the middle price in a limit order book) e-pool ibheka ku-LP's liquidity range. Uma ukuguqulwa kwama-marginal rate kuyinto i-stochastic, sinikeza indlela yokuguqulwa kwe-liquidity range ukwandisa i-fee revenue kanye ne-profit kusuka ku-changes eyenziwe ku-marginal rate. Ekugcineni, sinikeza idatha ye-Uniswap v3 ukuze kubonisa ukuthi, ngokuvamile, i-LP ibhizinisi ngempumelelo, futhi ukubonisa ukuthi ukusebenza kwe-out-of-sampling ye-strategy yethu iyahambisana ne-historical performance ye-LPs e-pool etholakalayo. Ukuhlolwa I-Electronic exchanges ezivamile ifakwe ngokuvumelana ne-limit order books ukuze ukunciphise isixazululo se-liquidity. Ngaphandle kwalokho, abathengisi abathengisi be-liquidity e-constant-function markets (CFMs) zihlanganisa ku-liquidity pools; abathengisi abathengisi be-liquidity (LPs) zihlanganisa izinsiza zabo ku-liquidity pool futhi abathengisi abathengisi be-liquidity (LTs) zihlanganisa izinsiza ngokuvumelana ne-pool. Kwangoku, i-CPMs (i-product markets) ne-concentrated liquidity (CLs) zihlanganisa uhlobo le-CFM, ne-Uniswap Kwi-CPM nge-CL, i-LP ibonise i-interval rates (isib. i-tick ranges) lapho i-asset yayo ibonise, futhi le-liquidity iyinhlangano yokuhweba kwe-LP lapho i-limit exchange rate ye-pool iyatholakala ku-liquidity range ye-LP. Uma i-LP ibonise i-liquidity, izindleko ezahlukile ze-LP zithunywe futhi zithunyelwe kwi-LP lapho zithunywe izindleko zayo kusuka ku-pool. I-LP ibonise izindleko zithunyelwe ku-LP iyahlukanyeka ngokuhambisana ne-liquidity esithunywe ku zonke izigaba ze-liquidity ze-pool. Ukuhlolwa okufakiwe kubaluleke imibuzo ye-LPs, kodwa ayikwazi ukunikezela izixhobo zokunikezela i-liquidity ye-strategic. Kule iphepha, sinqoke ukunikezela i-liquidity ye-strategic ku-CPMs nge-CL. Sinikeza i-dynamics ye-continuous-time ye-wealth ye-LPs ze-strategic okuyinto iqukethe isikhundla esithathwe ku-pool (i-value of position), i-fee income, ne-cost kusuka ku-repositioning isikhundla se-liquidity. Ukuphakama kwe-interval lapho ama-assets zihlanganisa kubaluleke i-value of the LP’s position in the pool; ngokuvamile, sinikeza ukuthi isisindo se-PL esithathwe njengoba ububanzi se-liquidity range ukunciphisa. I-PL ibonise izindleko ezingenalutho ze-LP asekelwe ku-depreciation ye-holdings zabo ku-pool kanye ne-opportunity costs kusuka ku-locking its assets in the pool; bheka Cartea et al. (2023b). I-PL kuyinto efana ne-loss-versus-rebalancing (LVR) ku-Milionis et al. (2022) okuyinto ibonisa izindleko ezivamile ze-CFMs lapho ama-LP zihlanganisa izindleko zayo emakethe e-exogenous.1 Ngaphezu kwalokho, sinikeza ukuthi imikhiqizo yama-fee iyatholakala ku-compromise phakathi kwebandhu ye-liquidity range ye-LP ne-volatility ye-marginal rate e-pool. Ngokuvamile, i-CL ikhiqiza imikhiqizo yama-fee lapho i-rate iyatholakala ku-LP, kodwa ukwandisa ingozi yokuhlanganisa. I-concentration risk ibizwa ku-risk eyenza i-LP lapho ibhizinisi yayo ibhizinisi emangalisayo emangalisayo; i-LP ibhizinisi ukuthatha izindleko lapho isivinini ivuka emangalisayo emangalisayo emangalisayo. Sinikeza isinyathelo se-dynamic enhle yokunikezela i-liquidity ku-CPM nge-CL. Kule imodeli yethu, i-LP ibhizinisi lokuphumelela okuphumelela kwezimpahla yayo ze-terminal, okuyinto zihlanganisa izindleko zebhizinisi zebhizinisi kanye nezinzuzo ze-marketing strategy. I-Dynamic Strategy isilawula ububanzi nokuhlukaniswa kwe-liquidity esihlanganisa i-exchange rate marginal. Ngokwesibonelo sokuxhumana kwe-log-utility, sinikeze i-strategy e-closed-form futhi ibonisa ukuthi isixazululo ivimbele imiphumela embalwa phakathi kwe-PL ne-fee collection. Uma i-volatility ivimbele, i-PL ivimbele, ngakho-ke kunezinto sokuvumela i-LP ukwandisa isixazululo se-liquidity ukuze ukunciphise isisindo se-PL. Ngokuvamile, ekupheleni kwe-volatility ephezulu kakhulu, i-LP kufuneka ivimbele kusuka ku-pool ngenxa yokuphendula kwe-PL. Ngaphezu kwalokho, lapho kukhona ukwandisa izindleko zokusebenza zokuqinisekiswa ukuthi i-LP ingatholela ngenxa yokushintshwa okuphezulu kwe-liquidity-taking activity, i-strategy ivimbele amaphuzu amabili abahlukile. Okokuqala, kukhona incentive ukwandisa izindleko zokushintshwa ngokuvimbela i-liquidity ye-LP eminyakeni eminyakeni eminyakeni ye-pool. Okokuqala, kukhona incentive ukunciphisa izindleko ngenxa yokushintshwa-risk ngokuvimbela ububanzi le-liquidity-taking. Ngemuva kwalokho, lapho isilinganiso se-marginal exchange rate kuyinto se-stochastic (isib. isignali yokubuyisa), i-strategy ivimbela i-liquidity range ukuze ukwandise i-fee revenue, ngokuvimbela i-LT trading flow, futhi ukwandisa i-position value, ngokuvimbela izinguquko ezihambayo se-marginal rate. Ngemuva kwalokho, thina usebenzisa i-Uniswap v3 idatha ukukhuthaza imodeli yethu futhi ukuhlola ukusebenza kwe-strategy etholakalayo. I-LP kanye ne-LT idatha ziye ku-pool ye-ETH/USDC (i-Ethereum ne-USD coin) phakathi kokuqala se-pool ngo-May 5, 2021 ne-Agasti 18, 2022. Ukuze ukubonisa ukusebenza kwe-strateji, sicela usebenzisa idatha e-sampling ukuze ukuguqulele ama-parameter yama-model kanye nama-out-of-sampling idatha ukuhlola i-strateji. Ukuhlolwa kwama-transactions e-Uniswap v3 ibonisa ukuthi i-LP yathengiswa ngezimali esikhulu, ngokuvamile, ku-ETH/USDC pool. Sinikeza ukuthi ukusebenza kwe-out-of-sampling ye-strateji ethu ikakhulu kunezimali ye-LP etholakalayo ku-ETH/USDC pool. Izifundo ezivamile ze-AMM zitholakala ku-Chiu and Koeppl (2019), i-Angeris et al. (2021), i-Lipton and Treccani (2021), i-Capponi and Jia (2021), i-Engel and Herlihy (2021a,b), i-Angeris et al. (2022); bheka futhi ukubuyekezwa okuvame ku-Biais et al. (2023). I-Capponi et al. (2023a) isifundo se-price formation ku-AMMs. I-Heimbach et al. (2022) isabela i-trade-off phakathi kwezinzuzo nezimali ezivela ku-Uniswap v3, i-Cartea et al. (2023b) isifundisa izindleko ezokufikelelekayo ze-LPs ku-continuous-time setting, i-Milionis et al. (2023) isifundisa imiphumela yemali ku-profit ye-arbitrageurs e-CFMs, i-Fukasawa et al. (2023) isifundisa i-heading ye-impermanent loss ye-LPs, futhi i-Lı et al. (2023) isifundisa i-economics ye-liquidity provision. Okugqithiselwe kwebhizinisi lethu, amamodeli e-Fan et al. (2021) noFan et al. (2022) okuyinto zihlanganisa imikhiqizo yama-fee kanye nokusetshenziswa kwezobugcisa zokuxhumana ukufinyelela izindlela zokudluliselwa. Okugqithiselwe, kukhona umbhalo olwandle ku-AMM yokukhipha phakathi kwe-LPs ne-LTs. I-Goyal et al. (2023) isifundisa i-AMM nge-functions zokudluliselwa zokudluliselwa okwenziwe nge-LPs, i-Lommers et al. (2023) isifundise i-AMM lapho isinyathelo se-LP isebenza ngokudluliselwa ngokudluliselwa kwebhizinisi, futhi i-Cartea Ukusebenzisana kwama-algorithmic trading kanye ne-optima market making literature. Iziqu ze-ho and Stoll (1983), i-Biais (1993), ne-Avelaneda ne-Stoikov (2008) nge-extensions ezininzi; bheka Cartea et al. (2014, 2017), Gueant' (2017), Bergault et al. (2021), Drissi (2022). Sinikeza umbhali ku-Cartea et al. (2015), i-Gueant' (2016), ne-Donnelly (2022) for a comprehensive review of algorithmic trading models for takers and makers of liquidity in traditional markets. Ngaphezu kwalokho, umsebenzi lethu lihlanganisa ne-Cartea et al. (2018), Barger and Lorig (2019), Cartea and Wang (2020), Donnelly and Lorig (2020), Forde et al. (2022), Bergault et al. (2022) okuyinto zihlanganisa ama-signals emakethe emakethe yokuhweba ye-algorithmic. I-residual ye-paper ithatha ngokulandelayo. Isigaba 2 ibonisa i-CL pools. Isigaba 3 isifundo se-dynamics eside-time ye-wealth ye-LPs ngenxa ye-position value, i-fee income, ne-rebalancing costs. Ngokuvamile, thina usebenzisa idatha ye-Uniswap v3 ukuhlola ingxenye yemali yentuthuko yentuthuko ye-LP futhi imiphumela yethu ithatha imibuzo emzimbeni yethu. Isigaba 4 ibonise imodeli yethu ye-liquidity provision futhi isetshenziselwa ukulawula kwe-stochastic ukuze afinyele isinyathelo esihle esifundeni esifundeni. Ngemuva kwalokho, thina ucwaninga indlela yokulawula ububanzi nokuhlukana kwe-liquidity range njenge-function of the pool's profitability, PL, risk of concentration, and the drift in the marginal rate. Okokuqala, Isigaba 5 isetshenziselwa idatha ye-Uniswap v3 ukuhlola ukusebenza kwe-strategy futhi ibonisa ukusebenza yayo engaphezulu. 
 
 Okuzenzakalelayo iyatholakala ku-archiv ngaphansi kwe-CC0 1.0 Universal License. Okuzenzakalelayo iyatholakala ku-archiv ngaphansi kwe-CC0 1.0 Universal License. ikhaya

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