Latency and liquidity provision in a limit order book

We use a recent, high-quality data set from Nasdaq to perform an empirical analysis of order flow in a limit order book 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 that some of our results are consistent 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 providers consider both adverse selection and expected waiting costs when deciding how to act.     

High-frequency trading and stock liquidity: An intraday analysis

This paper studies the impact of high-frequency trading (HFT) on intraday liquidity of CAC40 stocks listed on Euronext. Spreads display an intraday L-shaped pattern, while quoted depth follows an inverse pattern: low at the open and increasing towards the end of the trading day. When liquidity demand is particularly high, there is a high rate of order cancellations attributable to high-frequency traders who use frequent order cancellations to strategically manage their limit orders and close positions near the market close. Using the generalized method of moments estimator, we generate strong evidence that greater intensity of HFT is associated with lower spreads and higher depth. The positive effect of HFT on liquidity is due mainly to decreased adverse selection costs arising from asymmetric information among market participants.     

The optimal bid-ask price strategies of high-frequency trading and the effect on market liquidity

We propose a model for determining the optimal bid-ask spread strategy by a high-frequency trader (HFT) who has an informational advantage and receives information about the true value of a security. We employ an information cost function that includes volatility and the volume of the asset. Subsequently, we characterize the optimal bid-ask price strategies and obtain a stable bid-ask spread. We assume that orders submitted by low-frequency traders (LFTs) and news events arrive at the market with Poisson processes. Additionally, our model supports the trading of the two-sided quote in one period. We find that more LFTs and a higher exchange latency both hurt market liquidity. The HFT prefers to choose a two-sided quote to gain more profits while cautiously chooses a one-sided quote during times of high volatility. The model generates some testable implications with supporting empirical evidence from the NASDAQ-OMX Nordic Market.     

Price momentum in the New Zealand stock market: a proper accounting for transactions costs and risk*

We test for recently reported momentum profits in New Zealand using a practitioner technique that we have not yet seen in the academic literature. This technique simultaneously weighs returns, risk and transactions costs at each portfolio rebalance, rather than blindly chasing returns and then accounting for risk and transactions costs after the fact. We reverse the findings of the earlier literature because our gross profits are more than fully consumed once transactions costs are properly accounted for. Although we focus on momentum trading in New Zealand, our practitioner technique is broadly applicable to investigations of trading anomalies.     

Price impact and portfolio impact

We study survival, price impact, and portfolio impact in heterogeneous economies. We show that, under the equilibrium risk-neutral measure, long-run price impact is in fact equivalent to survival, whereas long-run portfolio impact is equivalent to survival under an agent-specific, wealth-forward measure. These results allow us to show that price impact and portfolio impact are two independent concepts: a nonsurviving agent with no long-run price impact can have a significant long-run impact on other agents' optimal portfolios.     

The diversity of high-frequency traders

The regulatory debate concerning high-frequency trading (HFT) emphasizes the importance of distinguishing different HFT strategies and their influence on market quality. Using data from NASDAQ-OMX Stockholm, we compare market-making HFTs to opportunistic HFTs. We find that market makers constitute the lion's share of HFT trading volume (63–72%) and limit order traffic (81–86%). Furthermore, market makers have higher order-to-trade ratios and lower latency than opportunistic HFTs. In a natural experiment based on tick size changes, we find that the activity of market-making HFTs mitigates intraday price volatility.     

Very fast money: High-frequency trading on the NASDAQ

This paper provides evidence regarding high-frequency trader (HFT) trading performance, trading costs, and effects on market efficiency using a sample of NASDAQ trades and quotes that directly identifies HFT participation. I find that HFTs engage in successful intra-day market timing, spreads are wider when HFTs provide liquidity and tighter when HFTs take liquidity, and prices incorporate information from order flow and market-wide returns more efficiently on days when HFT participation is high.     

Market making with minimum resting times

We show how the supply of liquidity in order-driven markets is affected if limit orders (LOs) are forced to rest in the limit order book for a minimum resting time (MRT) before they can be cancelled. The bid-ask spread increases as the MRT increases because market makers (MMs) increase the depth of their LOs to protect them from being picked off by other traders. We also show that the expected profits of the MMs increase when the MRT increases. The intuition is as follows. As the MRT increases, there are two opposing forces at work. One, the longer the MRT, the more likely the LOs are to be filled and, on average, shares are sold at a loss. Two, because the depth of the posted LOs increases, the probability that the LO is picked off by other traders before the end of the MRT decreases. The net effect is that a longer MRT leads to a higher expected profit. We also show that the depth of LOs increases when the volatility of the price of the asset increases. Also, the depth of LOs increases when the arrival rate of market orders increases because it is less likely that LOs will be picked off by the end of the MRT. Finally, our model also makes predictions about the overall liquidity of the market. We show that MMs choose to supply the minimum amount of shares per LO allowed by the exchange because expected profits are maximised when liquidity provided is lowest.     

Insider trading with correlation between liquidity trading and a public signal

We analyse a Kyle-type continuous-time market model in which liquidity trading is correlated with a noisy public signal that is released continuously. We show that, in contrast to the previous literature, Kyle's λ, the price sensitivity to the order flow, can even be non-monotonic, depending on the correlation structure. We also show that the introduction of an additional public signal does not necessarily improve the informational efficiency of the market, depending on the correlation.     

The non-linear market impact of large trades: evidence from buy-side order flow

We perform an empirical study of a set of large institutional orders executed in the US equity market. Our results validate the hidden order arbitrage theory proposed by Farmer et al. [How efficiency shapes market impact, 2013] of the market impact of large institutional orders. We find that large trades are drawn from a distribution with tail exponent of roughly 3/2 and that market impact approximately increases as the square root of trade duration. We examine price reversion after the completion of a trade, finding that permanent impact is also a square root function of trade duration and that its ratio to the total impact observed at the last fill is roughly 2/3. Additionally, we confirm empirically that the post-trade price reverts to a level consistent with a fair pricing condition of Farmer et al. (2013 Farmer, D., Gerig, A., Lillo, F. and Waelbroeck, H., How efficiency shapes market impact, 2013. Available online at: http://arxiv.org/abs/1102.5457 [Google Scholar]). We study the relaxation dynamics of market impact and find that impact decay is a multi-regime process, approximated by a power law in the first few minutes after order completion and subsequently by exponential decay.     

Optimal execution with non-linear transient market impact

We study the problem of the optimal execution of a large trade in the propagator model with non-linear transient impact. From brute force numerical optimization of the cost functional, we find that the optimal solution for a buy programme typically features a few short intense buying periods separated by long periods of weak selling. Indeed, in some cases, we find negative expected cost. We show that this undesirable characteristic of the non-linear transient impact model may be mitigated either by introducing a bid–ask spread cost or by imposing convexity of the instantaneous market impact function for large trading rates; the objective in each case is to robustify the solution in a parsimonious and natural way.     

The impact of short-selling and margin-buying on liquidity: Evidence from the Chinese stock market

We propose a framework based on limit order book to analyze the impact of short-selling and margin-buying on liquidity. We show that when short-sellers are perceived as informed, adverse selection may lead to uninformed traders withdrawing their limit orders. Given that the Chinese stock market has strong information asymmetry and a high proportion of uninformed traders, we predict that the pilot program launched in March 2010, which lifts restrictions on short-selling and margin-buying for a designated list of stocks, may have a negative impact on liquidity. We perform difference-in-differences tests and show evidence that allowing for short-selling and margin-buying indeed has a significantly negative impact on liquidity for stocks on the designated list. In particular, the negative impact on liquidity is more pronounced for stocks with high information asymmetry. Nevertheless, when short-selling volume dries up due to regulation changes in August 2015, i.e., the “T+1” trading rule on short-selling, we show that consistent with model predictions, lifting restrictions on short-selling and margin-buying has a positive effect on liquidity.     

A fully consistent,minimal model for non-linear market impact

We propose a minimal theory of non-linear price impact based on the fact that the (latent) order book is locally linear, as suggested by reaction–diffusion models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order that consistently generalizes previously proposed propagator models. We account for the universally observed square-root impact law, and predict non-trivial trajectories when trading is interrupted or reversed. We prove that our framework is free of price manipulation and that prices can be made diffusive (albeit with a generic short-term mean-reverting contribution). Our model suggests that prices can be decomposed into a transient ‘mechanical’ impact component and a permanent ‘informational’ component.     

Performance-weighted ensembles of random forests for predicting price impact

For any large player in financial markets, the impact of their trading activity represents a substantial proportion of transaction costs. This paper proposes a novel machine learning algorithm for predicting the price impact of order book events. Specifically, we introduce a prediction system based on ensembles of random forests (RFs). The system is trained and tested on depth-of-book data from the BATS and Chi-X exchanges and performance is benchmarked using ensembles of other popular regression algorithms including: linear regression, neural networks and support vector regression. The results show that recency-weighted ensembles of RFs produce over 15% greater prediction accuracy on out-of-sample data, for 5 out of 6 timeframes studied, compared with all benchmarks. Feature importance ranking is used to explore the significance of various market features on the price impact, finding them to be highly variable through time. Finally, a novel procedure for extracting the directional effects of features is proposed and used to explore the features most dominant in the price formation process.     

Low-latency trading

We define low-latency activity as strategies that respond to market events in the millisecond environment, the hallmark of proprietary trading by high-frequency traders though it could include other algorithmic activity as well. We propose a new measure of low-latency activity to investigate the impact of high-frequency trading on the market environment. Our measure is highly correlated with NASDAQ-constructed estimates of high-frequency trading, but it can be computed from widely-available message data. We use this measure to study how low-latency activity affects market quality both during normal market conditions and during a period of declining prices and heightened economic uncertainty. Our analysis suggests that increased low-latency activity improves traditional market quality measures—decreasing spreads, increasing displayed depth in the limit order book, and lowering short-term volatility. Our findings suggest that given the current market structure for U.S. equities, increased low-latency activity need not work to the detriment of long-term investors.     

Information-Based Trading and Price Improvement

Abstract:  In this study we test the information hypothesis of price improvement. Our results show that price improvement is negatively related to both the probability of information-based trading and the price impact of trades. We interpret these results as evidence that liquidity providers selectively offer price improvements according to the information content of trades. We also show that liquidity providers offer greater (and more frequent) price improvements when they are at the NBBO, and for stocks with wider spreads, fewer trades, or smaller trade sizes relative to the quoted depth. Buyer-initiated trades receive smaller (larger) price improvements than seller-initiated trades on the NYSE (NASDAQ).     

期货市场投资者行为与价格波动关系研究

通过从上海期货交易所获取数据,使用向量自回归检验了两种类型投资者的行为和价格波动性之间的关系.实证检验结果表明:(1)不同期货品种市场上的投机行为都会加剧价格波动性,而不同价格波动率度量方法下,套期保值行为对价格波动所产生的Granger显著影响只出现在某些期货品种市场上;(2)市场价格波动对套期保值行为没有显著的影响,而市场价格波动对投机者行为的影响则随着波动率的度量方法不同而不同.研究结论对于指导我国期货市场改善投资者结构、促进期货市场发展具有积极的意义.     

Cross-impact and no-dynamic-arbitrage

We extend the ‘No-dynamic-arbitrage and market impact’-framework of Gatheral [Quant. Finance, 2010, 10(7), 749–759] to the multi-dimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can be directly verified on data. For bounded decay kernels we find that cross-impact must be an odd and linear function of trading intensity and cross-impact from asset i to asset j must be equal to the one from j to i. To test these constraints we estimate cross-impact among sovereign bonds traded on the electronic platform MOT. While we find significant violations of the above symmetry condition of cross-impact, we show that these are not arbitrageable with simple strategies because of the presence of the bid-ask spread.     

Price formation,market quality and the effects of reduced latency in the very short run

Applying an innovative event study methodology to ultra short return horizons, this paper resolves market adjustment in the aftermath of corporate news events with unprecedented precision. It uncovers the ramifications of the reduction in latency of the German stock market on April 23rd 2007 and shows that it has had positive consequences for market quality. Analyzing second by second time windows the paper demonstrates that price determination, market efficiency as well as quoted spreads and order flow have significantly improved not only in broad average terms, but in particular during informative events.