Liquidity Provision

What Drives Liquidity on Decentralized Exchanges? Evidence from the Uniswap Protocol ArXiv ID: 2410.19107 “View on arXiv” Authors: Unknown Abstract We study liquidity on decentralized exchanges (DEXs), identifying factors at the platform, blockchain, token pair, and liquidity pool levels with predictive power for market depth metrics. We introduce the v2 counterfactual spread metric, a novel criterion which assesses the degree of liquidity concentration in pools using the ``concentrated liquidity’’ mechanism, allowing us to decompose the effect of a factor on market depth into two channels: total value locked (TVL) and concentration. We further explore how external liquidity from competing DEXs and private inventory on DEX aggregators influence market depth. We find that (i) gas prices, returns, and a DEX’s share of trading volume affect liquidity through concentration, (ii) internalization of order flow by private market makers affects TVL but not the overall market depth, and (iii) volatility, fee revenue, and markout affect liquidity through both channels. ...

Unified Approach for Hedging Impermanent Loss of Liquidity Provision ArXiv ID: 2407.05146 “View on arXiv” Authors: Unknown Abstract We develop static and dynamic approaches for hedging of the impermanent loss (IL) of liquidity provision (LP) staked at Decentralised Exchanges (DEXes) which employ Uniswap V2 and V3 protocols. We provide detailed definitions and formulas for computing the IL to unify different definitions occurring in the existing literature. We show that the IL can be seen a contingent claim with a non-linear payoff for a fixed maturity date. Thus, we introduce the contingent claim termed as IL protection claim which delivers the negative of IL payoff at the maturity date. We apply arbitrage-based methods for valuation and risk management of this claim. First, we develop the static model-independent replication method for the valuation of IL protection claim using traded European vanilla call and put options. We extend and generalize an existing method to show that the IL protection claim can be hedged perfectly with options if there is a liquid options market. Second, we develop the dynamic model-based approach for the valuation and hedging of IL protection claims under a risk-neutral measure. We derive analytic valuation formulas using a wide class of price dynamics for which the characteristic function is available under the risk-neutral measure. As base cases, we derive analytic valuation formulas for IL protection claim under the Black-Scholes-Merton model and the log-normal stochastic volatility model. We finally discuss estimation of risk-reward of LP staking using our results. ...

A Multi-step Approach for Minimizing Risk in Decentralized Exchanges ArXiv ID: 2406.07200 “View on arXiv” Authors: Unknown Abstract Decentralized Exchanges are becoming even more predominant in today’s finance. Driven by the need to study this phenomenon from an academic perspective, the SIAG/FME Code Quest 2023 was announced. Specifically, participating teams were asked to implement, in Python, the basic functions of an Automated Market Maker and a liquidity provision strategy in an Automated Market Maker to minimize the Conditional Value at Risk, a critical measure of investment risk. As the competition’s winning team, we highlight our approach in this work. In particular, as the dependence of the final return on the initial wealth distribution is highly non-linear, we cannot use standard ad-hoc approaches. Additionally, classical minimization techniques would require a significant computational load due to the cost of the target function. For these reasons, we propose a three-step approach. In the first step, the target function is approximated by a Kernel Ridge Regression. Then, the approximating function is minimized. In the final step, the previously discovered minimum is utilized as the starting point for directly optimizing the desired target function. By using this procedure, we can both reduce the computational complexity and increase the accuracy of the solution. Finally, the overall computational load is further reduced thanks to an algorithmic trick concerning the returns simulation and the usage of Cython. ...

A Tick-by-Tick Solution for Concentrated Liquidity Provisioning ArXiv ID: 2405.18728 “View on arXiv” Authors: Unknown Abstract Automated market makers with concentrated liquidity capabilities are programmable at the tick level. The maximization of earned fees, plus depreciated reserves, is a convex optimization problem whose vector solution gives the best provision of liquidity at each tick under a given set of parameter estimates for swap volume and price volatility. Surprisingly, early results show that concentrating liquidity around the current price is usually not the best strategy. ...

Data-driven measures of high-frequency trading ArXiv ID: 2405.08101 “View on arXiv” Authors: Unknown Abstract High-frequency trading (HFT) accounts for almost half of equity trading volume, yet it is not identified in public data. We develop novel data-driven measures of HFT activity that separate strategies that supply and demand liquidity. We train machine learning models to predict HFT activity observed in a proprietary dataset using concurrent public intraday data. Once trained on the dataset, these models generate HFT measures for the entire U.S. stock universe from 2010 to 2023. Our measures outperform conventional proxies, which struggle to capture HFT’s time dynamics. We further validate them using shocks to HFT activity, including latency arbitrage, exchange speed bumps, and data feed upgrades. Finally, our measures reveal how HFT affects fundamental information acquisition. Liquidity-supplying HFTs improve price discovery around earnings announcements while liquidity-demanding strategies impede it. ...

am-AMM: An Auction-Managed Automated Market Maker ArXiv ID: 2403.03367 “View on arXiv” Authors: Unknown Abstract Automated market makers (AMMs) have emerged as the dominant market mechanism for trading on decentralized exchanges implemented on blockchains. This paper presents a single mechanism that targets two important unsolved problems for AMMs: reducing losses to informed orderflow, and maximizing revenue from uninformed orderflow. The auction-managed AMM'' works by running a censorship-resistant onchain auction for the right to temporarily act as pool manager’’ for a constant-product AMM. The pool manager sets the swap fee rate on the pool, and also receives the accrued fees from swaps. The pool manager can exclusively capture some arbitrage by trading against the pool in response to small price movements, and also can set swap fees incorporating price sensitivity of retail orderflow and adapting to changing market conditions, with the benefits from both ultimately accruing to liquidity providers. Liquidity providers can enter and exit the pool freely in response to changing rent, though they must pay a small fee on withdrawal. We prove that under certain assumptions, this AMM should have higher liquidity in equilibrium than any standard, fixed-fee AMM. ...

A Mean Field Game between Informed Traders and a Broker ArXiv ID: 2401.05257 “View on arXiv” Authors: Unknown Abstract We find closed-form solutions to the stochastic game between a broker and a mean-field of informed traders. In the finite player game, the informed traders observe a common signal and a private signal. The broker, on the other hand, observes the trading speed of each of his clients and provides liquidity to the informed traders. Each player in the game optimises wealth adjusted by inventory penalties. In the mean field version of the game, using a Gâteaux derivative approach, we characterise the solution to the game with a system of forward-backward stochastic differential equations that we solve explicitly. We find that the optimal trading strategy of the broker is linear on his own inventory, on the average inventory among informed traders, and on the common signal or the average trading speed of the informed traders. The Nash equilibrium we find helps informed traders decide how to use private information, and helps brokers decide how much of the order flow they should externalise or internalise when facing a large number of clients. ...

Dealer Strategies in Agent-Based Models ArXiv ID: 2312.05943 “View on arXiv” Authors: Unknown Abstract This paper explores the utility of agent-based simulations in realistically modelling market structures and sheds light on the nuances of optimal dealer strategies. It underscores the contrast between conclusions drawn from probabilistic modelling and agent-based simulations, but also highlights the importance of employing a realistic test bed to analyse intricate dynamics. This is achieved by extending the agent-based model for auction markets by \cite{“Chiarella.2008”} to include liquidity providers. By constantly and passively quoting, the dealers influence their own wealth but also have ramifications on the market as a whole and the other participating agents. Through synthetic market simulations, the optimal behaviour of different dealer strategies and their consequences on market dynamics are examined. The analysis reveals that dealers exhibiting greater risk aversion tend to yield better performance outcomes. The choice of quote sizes by dealers is strategy-dependent: one strategy demonstrates enhanced performance with larger quote sizes, whereas the other strategy show a better results with smaller ones. Increasing quote size shows positive influence on the market in terms of volatility and kurtosis with both dealer strategies. However, the impact stemming from larger risk aversion is mixed. While one of the dealer strategies shows no discernible effect, the other strategy results in mixed outcomes, encompassing both positive and negative effects. ...

Analysis of the RMM-01 Market Maker ArXiv ID: 2310.14320 “View on arXiv” Authors: Unknown Abstract Constant function market makers(CFMMS) are a popular market design for decentralized exchanges(DEX). Liquidity providers(LPs) supply the CFMMs with assets to enable trades. In exchange for providing this liquidity, an LP receives a token that replicates a payoff determined by the trading function used by the CFMM. In this paper, we study a time-dependent CFMM called RMM-01. The trading function for RMM-01 is chosen such that LPs recover the payoff of a Black–Scholes priced covered call. First, we introduce the general framework for CFMMs. After, we analyze the pricing properties of RMM-01. This includes the cost of price manipulation and the corresponding implications on arbitrage. Our first primary contribution is from examining the time-varying price properties of RMM-01 and determining parameter bounds when RMM-01 has a more stable price than Uniswap. Finally, we discuss combining lending protocols with RMM-01 to achieve other option payoffs which is our other primary contribution. ...

Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision ArXiv ID: 2309.08431 “View on arXiv” Authors: Unknown Abstract Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form optimal liquidity provision strategy where the width of the LP’s liquidity range is determined by the profitability of the pool (provision fees minus gas fees), the predictable losses (PL) of the LP’s position, and concentration risk. Concentration risk refers to the decrease in fee revenue if the marginal exchange rate (akin to the midprice in a limit order book) in the pool exits the LP’s range of liquidity. When the drift in the marginal rate is stochastic, we show how to optimally skew the range of liquidity to increase fee revenue and profit from the expected changes in the marginal rate. Finally, we use Uniswap v3 data to show that, on average, LPs have traded at a significant loss, and to show that the out-of-sample performance of our strategy is superior to the historical performance of LPs in the pool we consider. ...