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-price. We formulate the control problem of the exchange who wishes to modify the shape of the order book by increasing the volume at specific limits. Due to the particular nature of the SPDE control problem, we are able to characterize the solution with a classic Feynman-Kac representation theorem. Moreover, when studying the asymptotic behavior of the solution, a specific penalty function enables the exchange to obtain closed-form incentives at each limit of the order book. We study numerically the form of the incentives and their impact on the shape of the order book, and analyze the sensitivity of the incentives to the market parameters.
The role of algorithmic traders as arbitrageurs and their impact on price efficiency in the foreign exchange market are examined. Algorithmic traders do not improve price efficiency by detecting and exploiting mispriced currency pairs. On the contrary, algorithmic traders contribute to the creation of possible arbitrage opportunities as a byproduct of intensified competition among liquidity providers. On the other hand, the same market-making competition also prevents the creation of arbitrage opportunities via tightening of spread. Moreover, the leftover inventory problem impedes the implementation of round-trip arbitrage trades - thereby rendering many "arbitrage opportunities" that do appear spurious. The latter two factors explain the reduced occurrence of arbitrage opportunities under the increased algorithmic trading presence observed in data.
We develop a methodology which replicates in great accuracy the FTSE Russell indexes reconstitutions, including the quarterly rebalancings due to new initial public offerings (IPOs). While using only data available in the CRSP US Stock database for our index reconstruction, we demonstrate the accuracy of this methodology by comparing it to the original Russell US indexes for the time period between 1989 and 2019. A python package that generates the replicated indexes is also provided [A Micheli. pyndex - Russell index reconstruction package. Available at https: //github.com/alemicheli/pyndex.]. As an application, we use our index reconstruction protocol to compute the permanent and temporary price impact on the Russell 3000 annual additions and deletions, and on the quarterly additions of new IPOs. We find that the index portfolios following the Russell 3000 index and rebalanced on an annual basis are overall more crowded than those following the index on a quarterly basis. This phenomenon implies that transaction costs of indexing strategies could be significantly reduced by buying new IPOs additions in proximity to quarterly rebalance dates.
In this article, we provide a flexible framework for optimal trading in an asset listed on different venues. We take into account the dependencies between the imbalance and spread of the venues, and allow for partial execution of limit orders at different limits as well as market orders. We present a Bayesian update of the model parameters to take into account possibly changing market conditions and propose extensions to include short/long trading signals, market impact or hidden liquidity. To solve the stochastic control problem of the trader we apply the finite difference method and also develop a deep reinforcement learning algorithm allowing to consider more complex settings.
A point process model for order flows in limit order books is proposed, in which the conditional intensity is the product of a Hawkes component and a state-dependent factor. In the LOB context, state observations may include the observed imbalance or the observed spread. Full technical details for the computationally-efficient estimation of such a process are provided, using either direct likelihood maximization or EM-type estimation. Applications include models for bid and ask market orders, or for upwards and downwards price movements. Empirical results on multiple stocks traded in Euronext Paris underline the benefits of state-dependent formulations for LOB modeling, e.g. in terms of goodness-of-fit to financial data.
In this work, we introduce a multivariate Hawkes model with an explicit dependency on queue size aimed at modeling the stochastic time evolution of a single queue (best bid queue or best ask queue) of a limit order book. The order flow at a given best queue is modeled using a multivariate Hawkes process whose exogenous intensity depends on the current state on the queue. We provide an explicit way to calibrate this model with a Maximum-Likelihood method. Empirical results show that our model improves the description of the order flow properties and the shape of the queue distributions.
We introduce a simple framework in which market participants update their prior about an efficient price with a model-based learning process. We show that exponential intensities for the arrival of aggressive orders arise naturally in this setting. Our approach allows us to fully describe market dynamics in the case with Brownian efficient price and informed market takers. We are also able to revisit the emergence of market impact due to meta-order splitting, making several connections with existing literature.
In this study, we examine the trading activity and volatility of stocks influenced by the U.S. Securities and Exchange Commission's pilot program that increases tick sizes for various samples of stocks. The objective of the program is to improve the market quality of small-cap stocks, which have historically been relatively less liquid than other stocks. Using a difference-in-differences approach, we find that, relative to control stocks, the trading activity of pilot stocks does not appear to be meaningfully affected by the increase in tick sizes. Volatility, however, increases markedly for the pilot stocks compared to non-pilot stocks. These results are robust to the three different sets of pilot stocks, various rollout periods, and different control groups. We also find that pilot stocks tend to cluster on round increments of $0.05 more frequently than non-pilot stocks after the rollout periods. This is true particularly for pilot stocks that quote on $0.05 but trade on $0.01. To the extent that prices convey important information to market participants, these latter results suggest that the discreteness in prices imposed by the pilot program may adversely affect the informativeness of prices in equity markets.
The modeling of the limit order book is directly related to the assumptions on the behavior of real market participants. This paper is two-fold. We first present empirical findings that lay the ground for two improvements to these models. The first one is concerned with market participants by adding the additional dimension of informed market makers, whereas the second, and maybe more original one, addresses the race in the book between informed traders and informed market makers leading to different shapes of the order book. Namely, we build an agent-based model for the order book with four types of market participants: informed trader, noise trader, informed market makers and noise market makers. We build our model based on the Glosten-Milgrom approach and the most recent Huang-Rosenbaum-Saliba approach. We introduce a parameter capturing the race between informed liquidity traders and suppliers after a new information on the fundamental value of the asset. We then derive the whole "static" limit order book and its characteristics, namely, the bid-ask spread and volumes available at each level price- from the interactions between the agents and compare it with the pre-existing model. We then discuss the case where noise traders have an impact on the fundamental value of the asset and extend the model to take into account many kinds of informed market makers.
The new MiFID II regulation put in place in January 2018 has deeply modified the microstructure of European financial markets. In particular, new tick size tables have been created, leading to tick size modifications for hundreds of assets. In this work, we investigate the relevance of this new tick size regime for the assets traded on Euronext. To do so, we analyze the changes of transaction costs paid by investors under this new regulation. We find that from this viewpoint, MiFID II clearly induced an improvement of market quality.
We solve explicitly the Almgren-Chriss optimal liquidation problem where the stock price process follows a geometric Brownian motion. Our technique is to work in terms of cash and to use functional analysis tools. We show that this framework extends readily to the case of a stochastic drift for the price process and the liquidation of a portfolio.
We consider a market impact game for $n$ risk-averse agents that are competing in a market model with linear transient price impact and additional transaction costs. For both finite and infinite time horizons, the agents aim to minimize a mean-variance functional of their costs or to maximize the expected exponential utility of their revenues. We give explicit representations for corresponding Nash equilibria and prove uniqueness in the case of mean-variance optimization. A qualitative analysis of these Nash equilibria is conducted by means of numerical analysis.
The latent order book of [Donier et al., 2015, A fully consistent, minimal model for nonlinear market impact, Quantitative Finance 15(7), 1109–1121] is one of the most promising agent-based models for market impact. This work extends the minimal model by allowing agents to exhibit mean-reversion, a commonly observed pattern in real markets. This modification leads to new order book dynamics, which we explicitly study and analyze. Underlying our analysis is a mean-field assumption that views the order book through its average density. We show how price impact develops in this new model, providing a flexible family of solutions that can potentially be calibrated to real data. While no closed-form solution is provided, we complement our theoretical investigation with extensive numerical results, including a simulation scheme for the entire order book.
We show that the excessive use of hidden orders causes artificial price pressures and abnormal asset returns. Using a simple game-theoretical setting, we demonstrate that this effect naturally arises from mis-coordination in trading schedules between traders, when suppliers of liquidity do not sufficiently disclose their trade intentions. As a result, hidden liquidity can increase trading costs and induce excess price fluctuations unrelated to information. Using NASDAQ order book data, we find strong empirical support and illustrate that hidden liquidity is higher if bid–ask spreads are smaller and relative tick sizes are higher.
We study optimal liquidation in “target zone models” — asset prices with a reflecting boundary enforced by regulatory interventions. This can be treated as a special case of an Almgren–Chriss model with running and terminal inventory costs and general predictive signals about price changes. The optimal liquidation rate in target-zone models can in turn be characterized as the “theta” of a lookback option, leading to explicit formulas for Bachelier or Black–Scholes dynamics.
Main objective of the study is to analyze firm characteristics which affect stock illiquidity. The paper aims to give suggestions and policy implications to corporates and investors while dealing with investments in illiquid stocks. ANOVA, chi-square tests, correlation analysis, univariate and multiple regression models are employed on Amihud (2002) (Amihud, Y., (2002). Illiquidity and Stock Returns: Cross-Section and Time-Series Effects, Journal of Financial Markets 5, 31–56) illiquidity measure and various firm characteristics. Findings of this paper suggest that firms with illiquid stocks can be characterized with low promoter’s stakes, high leverage, poor financial health, small size and low/negative profitability. The findings of the paper will be of relevance to retail investors who are at the mercy of informed investors. The results portray basic characteristics that an investor should look into before investing in any stock. The study is of value to the investors who are grieved because of the adverse selections and information asymmetry. Moreover, the basic nature of illiquid firms has never been studied.
This paper uses transaction data to estimate how single stock circuit breakers on the London Stock Exchange affect other stocks that remain in continuous trading. This "spillover" effect is estimated by calculating the effect of a trading halt on the market quality of stocks that remain in continuous trading and comparing this with the effect of a stock whose absolute returns are of a magnitude nearly sufficient to trigger a trading halt but do not do so. Market quality is measured using a combination of trading costs, volatility and volume. In the two-month period we study, characterized by a relatively volatile trading environment, we find that circuit breakers lead to a significant improvement in the liquidity, and reduction in the volatility, of stocks that remain in continuous trading. This suggests that - at least over the period covered by our data - single stock circuit breakers can play an important role in reducing the spillover of poor market quality across stocks.
This analysis investigates how liquidity is affected by periods of high trade intensity. Using an orderbook constructed directly from CME FIX/FAST messages and timestamped to the millisecond, we test whether the number of changes in the orderbook, the size of the bid–ask spread, and the number of trades in the few seconds before a trade have an effect on the book’s liquidity in the milliseconds after the trade. Since we calculate liquidity over a period of 100[Formula: see text]ms after a trade, we focus on liquidity provided by high-frequency traders (HFTs). We find evidence consistent with larger bid–ask spreads leading to greater amounts of liquidity being provided by HFT post-trade, and HFT providing liquidity when there is more activity in the orderbook. We further find that more trades lead to reduced liquidity, consistent with trades incorporating private information, and market makers’ fear of being adversely selected when providing liquidity.
We study the multi-level order-flow imbalance (MLOFI), which is a vector quantity that measures the net flow of buy and sell orders at different price levels in a limit order book (LOB). Using a recent, high-quality data set for six liquid stocks on Nasdaq, we fit a simple, linear relationship between MLOFI and the contemporaneous change in mid-price. For all six stocks that we study, we find that the out-of-sample goodness-of-fit of the relationship improves with each additional price level that we include in the MLOFI vector. Our results underline how order-flow activity deep into the LOB can influence the price-formation process.
We present an empirical study of price reversion after the executed metaorders. We use a dataset with more than 8 million metaorders executed by institutional investors in the US equity market. We show that relaxation takes place as soon as the metaorder ends: while at the end of the same day, it is on average [Formula: see text] of the peak impact, the decay continues for the next few days, following a power-law function at short-time scales, and converges to a non-zero asymptotic value at long-time scales ([Formula: see text] days) equal to [Formula: see text] of the impact at the end of the first day, that is [Formula: see text] of peak impact. Due to a significant, multiday correlation of the sign of executed metaorders, a careful deconvolution of the observed impact must be performed to extract the estimate of the impact decay of isolated metaorders.
