The price impact of order book events: market orders,limit orders and cancellations

While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different events, and their respective impact on future price changes. We define and extract from the data the ‘bare’ impact these events would have if they were to happen in isolation. For large tick stocks, we show that a model where the bare impact of all events is permanent and non-fluctuating is in good agreement with the data. For small tick stocks, however, bare impacts must contain a history-dependent part, reflecting the internal fluctuations of the order book. We show that this effect can be accurately described by an autoregressive model of the past order flow. This framework allows us to decompose the impact of an event into three parts: an instantaneous jump component, the modification of the future rates of the different events, and the modification of the jump sizes of future events. We compare in detail the present formalism with the temporary impact model that was proposed earlier to describe the impact of market orders when other types of events are not observed. Finally, we extend the model to describe the dynamics of the bid–ask spread.     

International order flows: Explaining equity and exchange rate returns

Macroeconomic models of equity and exchange rate returns perform poorly at high frequencies. The proportion of daily returns that these models explain is essentially zero. Instead of relying on macroeconomic determinants, we model equity price and exchange rate behavior based on a concept from microstructure–order flow. The international order flows are derived from belief changes of different investor groups in a two-country setting. We obtain a structural relationship between equity returns, exchange rate returns and their relationship to home and foreign equity market order flow. To test the model we construct daily aggregate order flow data from 800 million equity trades in the U.S. and France from 1999 to 2003. Almost 60% of the daily returns in the S&P100 index are explained jointly by exchange rate returns and aggregate order flows in both markets. As predicted by the model, daily exchange rate returns and order flow into the French market have significant incremental explanatory power for the daily S&P returns. The model implications are also validated for intraday returns.     

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.     

Price impact and bursts in liquidity provision

This paper analyses brief episodes of high-intensity quote turnover and revision—‘bursts’ in quotes—in the US equity market. Such events occur very frequently, several hundred times a day for actively traded stocks. We find significant price impact associated with these market maker initiated events, about five times higher than during non-burst periods. Bursts in quotes are concurrent with short-lived structural breaks in the informational relationship between market makers and market takers. During bursts, market makers no longer passively impound information from order flow into quotes—a departure from the traditional market microstructure paradigm. Rather, market makers significantly impact prices during bursts in quotes. Further analysis shows that there is asymmetry in adverse selection between the bid and ask sides of the limit order book and only a sub-population of market makers enjoys an informational advantage during bursts. Market makers on the side opposite the burst suffer elevated adverse selection costs, while market makers on the side of the burst realize positive spread, irrespective of the order flow direction. Our results call attention to the need for a new microstructure perspective in understanding modern high-frequency limit order book markets and the quote manipulation strategies at the disposal of the fast market makers.     

Market impact as anticipation of the order flow imbalance

In this paper, we assume that the permanent market impact of metaorders is linear and that the price is a martingale. Those two hypotheses enable us to derive the evolution of the price from the dynamics of the flow of market orders. For example, if the market order flow is assumed to follow a nearly unstable Hawkes process, we retrieve the apparent long memory of the flow together with a power law impact function, which is consistent with the celebrated square root law. We also link the long memory exponent of the sign of market orders with the impact function exponent. One of the originalities of our approach is that our results are derived without assuming that market participants are able to detect the beginning of metaorders.     

Fluctuations and response in financial markets: the subtle nature of ‘random’ price changes

Using trades and quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delilcated interplay between two opposite tendencies: long-range correlated market orders that lead to super-diffusion (or persistence), and mean revrting limit orders that lead to sub-diffusion (or anti-persistence). We define and study a model where the price, at any instant, is the result of the impact of all past trades, mediated by a non-constant ‘propagator’ in time that describes the response of the market to a single trade. Within this model, the market is shown to be, in a precise sense, at a critical point, where the price is purely diffusive and the average response function almost constant. We find empirically, and discuss theoretically, a fluctuation-response relation. We also discuss the fraction of truly informed market orders, that correctly anticipate short-term moves, and find that it is quite small.     

Estimation of zero-intelligence models by L1 data

A unit volume zero-intelligence (ZI) model is defined and the distribution of its L1 process is recursively described. Further, a generalized ZI model allowing non-unit market orders, shifts of quotes and general in-spread events is proposed and a formula for the conditional distribution of its quotes is given, together with a formula for price impact. For both the models, MLE estimators are formulated and shown to be consistent and asymptotically normal. Consequently, the estimators are applied to data of six US stocks from nine electronic markets. It is found that more complex variants of the models, despite being significant, do not give considerably better predictions than their simple versions with constant intensities.     

Is market impact a measure of the information value of trades? Market response to liquidity vs. informed metaorders

We examine a data-set of institutional trades where approximately one-fourth of the trades were labelled as having been created for cash flow purposes. We aggregate near-overlapping trades into metaorders and consider information, market impact and metaorder size. We find that during the execution, the functional form and scale of market impact are similar for cash flows and other metaorders. Differences arise in the price reversion following the end of a metaorder. For cash flows, presumed to have no true information content, the impact reverts almost completely on average in two to five days. For other metaorders, we find that reversion erases about one-third of the peak impact: for each size, price reverts to the average execution price, leaving no immediate profits after accounting for trading costs. Observed mark-to-market profits on metaorders that aggregate multiple portfolio manager orders, new metaorders and Nasdaq-listed stocks suggest that these metaorders are more informed than the average. Vice-versa, we find mark-to-market losses are more likely to occur on cash flows, metaorders in large-cap stocks, metaorders that follow momentum and additions to a prior position seeking to take advantage of an improved price. The complete price reversion for cash flows suggests that the mechanical permanent impact that is considered in no-quasi-arbitrage arguments would be much smaller than the information in typical institutional metaorders.     

The impact of share price on seasonality and size anomalies in Australian equity returns

Given the high correlation between a firm's stock price and market capitalisation, it is possible that the well-documented size anomaly is masking a share-price effect. Using a seemingly unrelated regression model to accommodate contemporaneous correlation between portfolios, we estimate the separate effects of firm size and share price on returns to Australian equity portfolios. The analysis is also extended to estimate seasonal components of size and price effects. Our major findings are: (i) firm size and share price have significant and independent effects on portfolio returns averaged over all months, (ii) the familiar negative relation between size and returns is confirmed across all months, and (iii) the relation between share price and returns is negative in July and positive in all other months (with the exception of January where no price effect occurs). These findings, which are consistent across sub-periods and robust to method variations, highlight the need for future research to provide an economic foundation for the relation between average returns, size and price.     

Volatility Clustering, Asymmetry and Hysteresis in Stock Returns: International Evidence

Encompassing a very broad family of ARCH-GARCH models, we show that the AT-GARCH (1,1) model, where volatility rises more in response to bad newsthan to good news, and where news are considered bad only below a certain level, is a remarkably robust representation of worldwide stock market returns. The residual structure is then captured by extending ATGARCH (1,1) to an hysteresis model, HGARCH, where we modelstructured memory effects from past innovations. Obviously, this feature relates to the psychology of the markets and the way traders process information. For the French stock market we show that votalitity is affected differently, depending on the recent past being characterized by returns all above or below a certain level. In the same way a longer term trend may also influence volatility. It is found that bad news are discounted very quickly in volatility, this effect being reinforced when it comes after a negative trend in the stock index. On the opposite, good news have a very small impact on volatility except when they are clustered over a few days, which in this case reduces volatility.     

How efficiency shapes market impact

We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e. the impact per share of large metaorders is smaller than that of small metaorders. We formulate a stylized model of an algorithmic execution service and derive a fair pricing condition, which says that the average transaction price of the metaorder is equal to the price after trading is completed. We show that at equilibrium the distribution of trading volume adjusts to reflect information, and dictates the shape of the impact function. The resulting theory makes empirically testable predictions for the functional form of both the temporary and permanent components of market impact. Based on the commonly observed asymptotic distribution for the volume of large trades, it says that market impact should increase asymptotically roughly as the square root of metaorder size, with average permanent impact relaxing to about two-thirds of peak impact.     

Determinants of bid and ask quotes and implications for the cost of trading

Financial transaction costs are time varying. This paper proposes a model that relates transaction cost to characteristics of order flow. We obtain qualitatively consistent model results for different stocks and across different time periods. We find that an unusual excess of buyers (sellers) relative to sellers (buyers) tends to increase the ask (bid) price. Hence, the ask and bid components of spread change asymmetrically about the efficient price. For a fixed order imbalance surprise these effects are muted when unanticipated total volume is high. Unexpected high volatility in the transaction price process tends to widen the spread symmetrically about the efficient price. Our findings are consistent with predications from market microstructure theory that the cost of market making should depend on both the risk of trading with better-informed traders and inventory risk. We also find that order flow surprises have a significant impact on the efficient price and can also explain a substantial amount of persistence in the volatility of the efficient price. This dependence does not violate the efficient market hypothesis since the surprises, by definition, are not predictable.     

The determinants of the price impact of block trades: further evidence

This article extends previous literature which examines the determinants of the price impact of block trades on the Australian Stock Exchange. As previous literature suggests that liquidity exhibits intraday patterns, we introduce time of day dummy variables to explore time dependencies in price impact. Following theoretical developments in previous literature, the explanatory power of the bid–ask spread, a lagged cumulative stock return variable and a refined measure of market returns are also examined. The model estimated explains approximately 29 per cent of the variation in price impact. Block trades executed in the first hour of trading experience the greatest price impact, while market conditions, lagged stock returns and bid–ask spreads are positively related to price impact. The bid–ask spread provides most of the explanatory power. This suggests that liquidity is the main driver of price impact.     

Universal price impact functions of individual trades in an order-driven market

The trade size ω has a direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization C is included as an argument in the scaling relation. However, the rationale of introducing stock capitalization in the scaling is unclear and the anomalous negative correlation between price change r and trade size ω for small trades is unexplained. Here we show that these issues can be addressed by taking into account the aggressiveness of orders that result in trades together with a proper normalization technique. Using order book data from the Chinese market, we show that trades from filled and partially filled limit orders have very different price impacts. The price impact of trades from partially filled orders is constant when the volume is not too large, while that of filled orders shows power-law behavior r?～?ω^α with α?≈?2/3. When returns and volumes are normalized by stock-dependent averages, capitalization-independent scaling laws emerge for both types of trades. However, no scaling relation in terms of stock capitalization can be constructed. In addition, the relation α?=?α_ω/α _r is verified for some individual stocks and for the whole data set containing all stocks using partially filled trades, where α_ω and α _r are the tail exponents of trade sizes and returns. These observations also enable us to explain the anomalous negative correlation between r and ω for small-size trades.     

Hawkes model for price and trades high-frequency dynamics

We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by four kernels associated with, respectively, the trade arrival self-excitation, the price changes mean reversion, the impact of trade arrivals on price variations and the feedback of price changes on trading activity. It allows one to account for both stylized facts of market price microstructure (including random time arrival of price moves, discrete price grid, high-frequency mean reversion, correlation functions behaviour at various time scales) and the stylized facts of market impact (mainly the concave-square-root-like/relaxation characteristic shape of the market impact of a meta-order). Moreover, it allows one to estimate the entire market impact profile from anonymous market data. We show that these kernels can be empirically estimated from the empirical conditional mean intensities. We provide numerical examples, application to real data and comparisons to former approaches.     

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 securitization of gold and its potential impact on gold stocks

We study the market impact of a very successful financial innovation – the SPDR Gold Trust exchange-traded fund (GLD). GLD holds physical gold, and provides traders with a convenient and cost-effective way to gain exposure to gold. We find that after the introduction of GLD, the liquidity of gold company stocks declined, and their adverse-selection risk increased. Over the two-month period after GLD’s introduction, the stocks’ relative effective bid-ask spreads increased by over 15%, while their adverse-selection cost, as measured by the price impact of trades, went up by more than 30%. Gold stocks also experienced significant negative abnormal returns (−12% on average) in the month after GLD started trading. Our findings suggest that GLD attracted traders, especially uninformed traders, away from gold company stocks, and that the resulting negative demand shocks and decrease in the stocks’ liquidity caused their prices to decline. Our results show that existing securities can be seriously adversely affected when a new security enters the market.     

Universal features of price formation in financial markets: perspectives from deep learning

Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary relation between order flow history and the direction of price moves. The universal price formation model exhibits a remarkably stable out-of-sample accuracy across a wide range of stocks and time periods. Interestingly, these results also hold for stocks which are not part of the training sample, showing that the relations captured by the model are universal and not asset-specific.

The universal model—trained on data from all stocks—outperforms asset-specific models trained on time series of any given stock. This weighs in favor of pooling together financial data from various stocks, rather than designing asset- or sector-specific models, as is currently commonly done. Standard data normalizations based on volatility, price level or average spread, or partitioning the training data into sectors or categories such as large/small tick stocks, do not improve training results. On the other hand, inclusion of price and order flow history over many past observations improves forecast accuracy, indicating that there is path-dependence in price dynamics.     

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.