Traditional market makers are losing their importance as automated systems have largely assumed the role of liquidity provision in markets. We update the model of Glosten and Milgrom (1985) to analyze this new world: we add multiple securities and introduce an automated market maker who uses the relationships between securities to price order flow. This new automated participant transacts the majority of orders, sets prices that are more efficient, and increases informed and decreases uninformed traders' transaction costs. These results can explain the recent dominance of high frequency trading in US markets and the corresponding increase in trading volume and decrease in transaction costs for US stocks.
We use a recent, high-quality data set from Nasdaq to perform an empirical analysis of order flow in a limit order book (LOB) before and after the arrival of a market order. For each of the stocks that we study, we identify a sequence of distinct phases across which the net flow of orders differs considerably. We note some of our results are consist with the widely reported phenomenon of stimulated refill, but that others are not. We therefore propose alternative mechanical and strategic motivations for the behaviour that we observe. Based on our findings, we argue that strategic liquidity pro…
Previous research has found that high-frequency traders will vary the bid or offer price rapidly over periods of milliseconds. This is a benefit to fast traders who can time their trades with microsecond precision, however it is a cost to the average market participant due to increased trade execution price uncertainty. In this analysis we attempt to construct real-time methods for determining whether the liquidity of a security is being altered rapidly. We find a four-state Markov switching model identifies a state where liquidity is being rapidly varied about a mean value. This state can be …
A small investor provides liquidity at the best bid and ask prices of a limit order market. For small spreads and frequent orders of other market participants, we explicitly determine the investor's optimal policy and welfare. In doing so, we allow for general dynamics of the mid price, the spread, and the order flow, as well as for arbitrary preferences of the liquidity provider under consideration.
We study one-shot Nash competition between an arbitrary number of identical dealers that compete for the order flow of a client. The client trades either because of proprietary information, exposure to idiosyncratic risk, or a mix of both trading motives. When quoting their price schedules, the dealers do not know the client's type but only its distribution, and in turn choose their price quotes to mitigate between adverse selection and inventory costs. Under essentially minimal conditions, we show that a unique symmetric Nash equilibrium exists and can be characterized by the solution of a no…
The standard approach for compensating liquidity providers on many decentralized exchanges (DEX) for serving as counter-party to swaps is through charging a small percentage of fees. The expected payoff from the cash flow of this mode of market making has yet to be mathematically formulated in terms of volatility in the existing literature. We provide here a preliminary derivation of the payoff formula, by making the standard set of assumptions for efficient markets, namely geometric Brownian price movements and zero arbitrage. Trading volume, conventionally taken as an exogenous variable for …
We investigate whether the fee income from trades on the CFM is sufficient for the liquidity providers to hedge away the exposure to market risk. We first analyse this problem through the lens of continuous-time financial mathematics and derive an upper bound for not-arbitrage fee income that would make CFM efficient and liquidity provision fair. We then evaluate our findings by performing multi-agent simulations by varying CFM fees, market volatility, and rate of arrival of liquidity takers. We observe that, on average, fee income generated from liquidity provision is insufficient to compensa…
Liquidity providers are essential for the function of decentralized exchanges to ensure liquidity takers can be guaranteed a counterparty for their trades. However, liquidity providers investing in liquidity pools face many risks, the most prominent of which is impermanent loss. Currently, analysis of this metric is difficult to conduct due to different market maker algorithms, fee structures and concentrated liquidity dynamics across the various exchanges. To this end, we provide a framework to generalize impermanent loss for multiple asset pools obeying any constant function market maker wit…
We analyse two models of liquidity provision to determine the retail traders' preference for marketable order routing. Order internalization is captured by a model of market makers competing for the retail order flow in a Bertrand fashion. On the other hand, the price-taking competitive liquidity providers characterize the open exchange model. We show that, when liquidity providers are risk averse, routing of the marketable orders to the wholesalers is preferred by all retail traders: informed, uninformed and noisy. The unwillingness of liquidity providers to bear risk causes the strategic tra…
Is Trend Still Your Friend?: A Microstructural Account of the Demise of Short-Term Trend-Following
Institut Louis Bachelier（路易·巴舍利耶研究所）；École polytechnique（巴黎综合理工学院）；Imperial College London（伦敦帝国学院）；Capital Fund Management（资本基金管理公司）；Académie des Sciences（科学院）
The study proposes a quote-driven predictive automated market maker (AMM) platform with on-chain custody and settlement functions, alongside off-chain predictive reinforcement learning capabilities to improve liquidity provision of real-world AMMs. The proposed AMM architecture is an augmentation to the Uniswap V3, a cryptocurrency AMM protocol, by utilizing a novel market equilibrium pricing for reduced divergence and slippage loss. Further, the proposed architecture involves a predictive AMM capability, utilizing a deep hybrid Long Short-Term Memory (LSTM) and Q-learning reinforcement learni…
We present an empirical study of the intertwined behaviour of members in a financial market. Exploiting a database where the broker that initiates an order book event can be identified, we decompose the correlation and response functions into contributions coming from different market participants and study how their behaviour is interconnected. We find evidence that (1) brokers are very heterogeneous in liquidity provision -- some are consistently liquidity providers while others are consistently liquidity takers. (2) The behaviour of brokers is strongly conditioned on the actions of {\it oth…
This paper develops a model of liquidity provision in financial markets by adapting the Madhavan, Richardson, and Roomans (1997) price formation model to realistic order books with quote discretization and liquidity rebates. We postulate that liquidity providers observe a fundamental price which is continuous, efficient, and can assume values outside the interval spanned by the best quotes. We confirm the predictions of our price formation model with extensive empirical tests on large high-frequency datasets of 100 liquid Nasdaq stocks. Finally we use the model to propose an estimator of the f…
Liquidity and trading activity on constant function market makers (CFMMs) such as Uniswap, Curve, and Balancer has grown significantly in the second half of 2020. Much of the growth of these protocols has been driven by incentivized pools or 'yield farming', which reward participants in crypto assets for providing liquidity to CFMMs. As a result, CFMMs and associated protocols, which were historically very small markets, now constitute the most liquid trading venues for a large number of crypto assets. But what does it mean for a CFMM to be the most liquid market? In this paper, we propose a b…
Automated market makers (AMM) have grown to obtain significant market share within the cryptocurrency ecosystem, resulting in a proliferation of new products pursuing exotic strategies for horizontal differentiation. Yet, their theoretical properties are curiously homogeneous when a set of basic assumptions are met. In this paper, we start by presenting a universal approach to deriving a formula for liquidity provisioning for AMMs. Next, we show that the constant function market maker and token swap market maker models are theoretically equivalent when liquidity reserves are uniform. Proceedin…
With the fragmentation of electronic markets, exchanges are now competing in order to attract trading activity on their platform. Consequently, they developed several regulatory tools to control liquidity provision / consumption on their liquidity pool. In this paper, we study the problem of an exchange using incentives in order to increase market liquidity. We model the limit order book as the solution of a stochastic partial differential equation (SPDE) as in [12]. The incentives proposed to the market participants are functions of the time and the distance of their limit order to the mid-pr…
How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different timescales. Here we reveal that price impact has a universal non-linear shape for trades aggregated on any intra-day scale. Its shape varies little across instruments, but drastically different master curves are obtained for order-volume and -sign impact. The scaling is largely determined by the relevant Hurst exponents. We further show that extreme order flow imbalance is not associated with lar…
Biondi et al. (2012) develop an analytical model to examine the emergent dynamic properties of share market price formation over time, capable to capture important stylized facts. These latter properties prove to be sensitive to regulatory regimes for fundamental information provision, as well as to market confidence conditions among actual and potential investors. Regimes based upon mark-to-market (fair value) measurement of traded security, while generating higher linear correlation between market prices and fundamental signals, also involve higher market instability and volatility. These re…
Oft-cited causes of mini-flash crashes include human errors, endogenous feedback loops, the nature of modern liquidity provision, fundamental value shocks, and market fragmentation. We develop a mathematical model which captures aspects of the first three explanations. Empirical features of recent mini-flash crashes are present in our framework. For example, there are periods when no such events will occur. If they do, even just before their onset, market participants may not know with certainty that a disruption will unfold. Our mini-flash crashes can materialize in both low and high trading …
