Can order exposure be mandated?

In this paper, we examine whether the hidden portion of limit orders represents depth that would be revealed if traders were not allowed to hide it, and the associated market quality implications. Specifically, we examine the decisions by the Toronto Stock Exchange to first abolish the use of hidden limit orders in 1996, and then reintroduce them in 2002. We find that quoted depth does not change following either decision, suggesting that the hidden portion of orders represents depth that would otherwise not be exposed. Using confidential order data for the period following the reintroduction of hidden limit orders, we find that total inside depth increases. For both events, volume does not change and the usage of the limit order book increases if hidden limit orders are allowed. This suggests that if traders are required to expose their orders they will not exit the market, but instead will switch to using market orders. We also find evidence to suggest that informed traders use hidden limit orders to minimize price impact if the probability of non-execution is small.     

The role of volume in order book dynamics: a multivariate Hawkes process analysis

We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy [IEEE Trans. Inform. Theory, 2016, 62, 2184–2202] can be successfully used to study complex interactions between the time of arrival of orders and their size observed in a limit order book market. We apply this methodology to high-frequency order book data of futures traded at EUREX. Specifically, we demonstrate how this approach is amenable not only to analyse interplay between different order types (market orders, limit orders, cancellations) but also to include other relevant quantities, such as the order size, into the analysis, showing also that simple models assuming the independence between volume and time are not suitable to describe the data.     

Limit order books and trade informativeness

In the microstructure literature, information asymmetry is an important determinant of market liquidity. The classic setting is that uninformed dedicated liquidity suppliers charge price concessions when incoming market orders are likely to be informationally motivated. In limit order book (LOB) markets, however, this relationship is less clear, as market participants can switch roles, and freely choose to immediately demand or patiently supply liquidity by submitting either market or limit orders. We study the importance of information asymmetry in LOBs based on a recent sample of 30 German Deutscher Aktienindex (DAX) stocks. We find that Hasbrouck's (1991) measure of trade informativeness Granger causes book liquidity, in particular that required to fill large market orders. Picking-off risk due to public news-induced volatility is more important for top-of-the book liquidity supply. In our multivariate analysis, we control for volatility, trading volume, trading intensity and order imbalance to isolate the effect of trade informativeness on book liquidity.     

Hybrid markets, tick size and investor trading costs

This paper shows how the tick size affects equilibrium outcomes in a hybrid stock market such as the NYSE that features both a specialist and a limit order book. Reducing the tick size facilitates the specialist's ability to step ahead of the limit order book, resulting in a reduction in the cumulative depth of the limit order book at prices above the minimum tick. If market demand is price-sensitive, and there are costs of limit order submission, the limit order book can be destroyed by tick sizes that are either too small or too large. We show that trading cost is minimized at larger tick sizes for larger market orders, creating an incentive to submit smaller orders when tick size is reduced. With a smaller tick size, specialist participation increases and specialist profit increases slightly for small market orders, and considerably for large market orders.     

More on a statistical analysis of log-periodic precursors to financial crashes

In this paper, we extend the existing empirical evidence on the relationship between the state of the limit order book (LOB) and order choice. Our contribution is twofold: first, we propose a sequential ordered probit (SOP) model which allows studying patient and impatient traders’ choices separately; second, we consider two pieces of LOB information, the best quotes and the book beyond the best quotes. We find that both pieces of LOB information explain the degree of patience of an incoming trader and, afterwards, its order choice. Nonetheless, the best quotes concentrate most of the explanatory power of the LOB. The shape of the book beyond the best quotes is crucial in explaining the aggressiveness of patient (limit order) traders, while impatient (market order) traders base their decisions primarily on the best quotes. Patient traders’ choices depend more on the state of the LOB on the same side of the market, while impatient traders mostly look at the state of the LOB on the opposite side. The aggressiveness of both types of traders augments with the inside spread. However, patient (impatient) traders submit more (less) aggressive limit (market) orders when the depth of the own (opposite) best quote and the length of the own (opposite) side of the book increase. We also find that higher depth away from the best ask (bid) quote may signal that this quote is ‘too low (high)’, causing incoming impatient buyers (sellers) to be more aggressive and incoming patient sellers (buyers) to be more conservative.     

Hidden Liquidity: Some New Light on Dark Trading

Using a laboratory market, we investigate how the ability to hide orders affects traders’ strategies and market outcomes in a limit order book environment. We find that order strategies are greatly affected by allowing hidden liquidity, with traders substituting nondisplayed for displayed shares and changing the aggressiveness of their trading. As traders adapt their behavior to the different opacity regimes, however, most aggregate market outcomes (such as liquidity and informational efficiency) are not affected as much. We also find that opacity appears to increase the profits of informed traders but only when their private information is very valuable.     

Upstairs Market for Principal and Agency Trades: Analysis of Adverse Information and Price Effects

This paper directly tests the hypothesis that upstairs intermediation lowers adverse selection cost. We find upstairs market makers effectively screen out information-motivated orders and execute large liquidity-motivated orders at a lower cost than the downstairs market. Upstairs markets do not cannibalize or free ride off the downstairs market. In one-quarter of the trades, the upstairs market offers price improvement over the limit orders available in the consolidated limit order book. Trades are more likely to be executed upstairs at times when liquidity is lower in the downstairs market.     

Multiple-limit trades: empirical facts and application to lead–lag measures

Order splitting is a standard practice in trading: traders constantly scan the limit order book and choose to limit the size of their market orders to the quantity available at the best limit, thereby controlling the market impact of their orders. In this article, we focus on the other trades, multiple-limit trades that go through the best available price in the order book, or ‘trade-throughs’. We provide various statistics on trade-throughs: frequency, volume, intraday distribution, market impact, etc., and present a new method for the measurement of lead–lag parameters between assets, sectors or markets.     

Limit Orders, Depth, and Volatility: Evidence from the Stock Exchange of Hong Kong

We investigate the role of limit orders in the liquidity provision in a pure order-driven market. Results show that market depth rises subsequent to an increase in transitory volatility, and transitory volatility declines subsequent to an increase in market depth. We also examine how transitory volatility affects the mix between limit orders and market orders. When transitory volatility arises from the ask (bid) side, investors will submit more limit sell (buy) orders than market sell (buy) orders. This result is consistent with the existence of limit-order traders who enter the market and place orders when liquidity is needed.     

Competition,signaling and non-walking through the book: Effects on order choice

We investigate the effects of competition and signaling in a pure order driven market and examine the trading patterns of agents when walking through the book is not allowed. Our results suggest that the variables capturing the cost of a large market order are not informative for an impatient trader under this market mechanism. We also document that the competition effect is not present only at the top of the book but persistent beyond the best quotes. Moreover, it dominates the signaling effect for both a limit order and a market order trader. Finally, we show that institutional investors’ order submission strategies are characterized by only a few pieces of the limit order book information. This is consistent with informed traders placing orders based on their own private valuations rather than the state of the book.     

The total cost of trading Belgian shares: Brussels versus London

Since 1990, London’s SEAQ International (SEAQ-I) has attracted considerable trading volume in Belgian equities. This paper investigates competition between the Brussels CATS market and London’s SEAQ-I. Toward this end, we gathered extensive limit order book data as well as transactions and quotation information. With regard to liquidity (indirect costs), measured by the quoted and effective bid–ask spread, the paper concludes that CATS outperforms SEAQ International for both measures. The effective spread is of course substantially smaller than the quoted spread, with the CATS effective spread showing a U-shaped form. This paper, unique in employing an extensive data set that includes all hidden orders and the whole limit order book, produces results in line with the different market microstructure models. Total trading costs on CATS are lower (higher) for small (large) trade sizes.     

Specialist participation and limit orders

We present a market microstructure model to examine specialist's strategic participation decisions in a security market where there are noise traders, limit order traders, an insider and a specialist. We argue that the specialist's participation rate depends on the depth of the limit book and its uncertainty. In particular, the specialist has incentives to trade against the market trend when the limit book depth is low and to trade with the market trend when the depth is high. Moreover, the specialist's participation rate is positively related to the limit book depth uncertainty and the asset price volatility, but is negative related to the average trading volume. We also discuss the specialist's participation strategies under the NYSE regulation that prohibits the specialist from trading with the market trend.     

Optimal high-frequency trading with limit and market orders

We propose a framework for studying optimal market-making policies in a limit order book (LOB). The bid–ask spread of the LOB is modeled by a tick-valued continuous-time Markov chain. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at best bid (resp. ask) plus (resp. minus) a tick for obtaining execution order priority, which is a crucial issue in high-frequency trading. The agent faces an execution risk since her limit orders are executed only when they meet counterpart market orders. She is also subject to inventory risk due to price volatility when holding the risky asset. The agent can then also choose to trade with market orders, and therefore obtain immediate execution, but at a less favorable price. The objective of the market maker is to maximize her expected utility from revenue over a short-term horizon by a trade-off between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/impulse control problem that we characterize in terms of a quasi-variational system by dynamic programming methods. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. We provide an explicit backward splitting scheme for solving the problem and show how it can be reduced to a system of simple equations involving only the inventory and spread variables. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market orders.     

Liquidity,volume and price efficiency: The impact of order vs. quote driven trading

As equity trading becomes predominantly electronic, is there still value to a traditional, intermediated dealer system? We address this question by comparing the impact of the organization of trading on volume, liquidity, and price efficiency in a quote-driven dealer market and in an order-driven limit order book. Small order price impacts are higher and large order price impacts are lower in a dealer market. Prices are more efficient in the limit order book, except when the level of informed trading is high. Volume is higher in a limit order market, making this system most attractive for trading venues.     

Modelling the buy and sell intensity in a limit order book market

In this paper, we model the buy and sell arrival process in the limit order book market at the Australian Stock Exchange. Using a bivariate autoregressive intensity model we analyze the contemporaneous buy and sell intensity as a function of the state of the market. We find evidence that trading decisions are both information as well as liquidity driven. Confirming predictions from market microstructure theory traders submit market orders by inferring from the recent order flow and the book with respect to upper and lower tail expectations as well as trading directions. However, traders also tend to take liquidity when the liquidity supply is high. Moreover, we find evidence that traders pay more attention to recent order arrivals and the current state of the order book than to the past order flow.     

Undisclosed orders and optimal submission strategies in a limit order market

Reserve orders enable traders to hide a portion of their orders and now appear in most electronic limit order markets. This paper outlines a theory to determine an optimal submission strategy in a limit order book, in which traders choose among limit, market, and reserve orders and simultaneously set price, quantity, and exposure. We show that reserve orders help traders compete for the provision of liquidity and reduce the friction generated by exposure costs. Therefore, total gains from trade increase. Large traders always benefit from reserve orders, whereas small traders benefit only when the tick size is large.     

Implied Lévy volatility

We study the cause of large fluctuations in prices on the London Stock Exchange. This is done at the microscopic level of individual events, where an event is the placement or cancellation of an order to buy or sell. We show that price fluctuations caused by individual market orders are essentially independent of the volume of orders. Instead, large price fluctuations are driven by liquidity fluctuations, variations in the market's ability to absorb new orders. Even for the most liquid stocks there can be substantial gaps in the order book, corresponding to a block of adjacent price levels containing no quotes. When such a gap exists next to the best price, a new order can remove the best quote, triggering a large midpoint price change. Thus, the distribution of large price changes merely reflects the distribution of gaps in the limit order book. This is a finite size effect, caused by the granularity of order flow: in a market where participants place many small orders uniformly across prices, such large price fluctuations would not happen. We show that this also explains price fluctuations on longer timescales. In addition, we present results suggesting that the risk profile varies from stock to stock, and is not universal: lightly traded stocks tend to have more extreme risks.     

Whose trades convey information? Evidence from a cross-section of traders

This paper contributes empirically to our understanding of informed traders. It analyzes traders’ characteristics in a foreign exchange electronic limit order market via anonymous trader identities. We use six indicators of informed trading in a cross-sectional multivariate approach to identify traders with high price impact. More information is conveyed by those traders’ trades which—simultaneously—use medium-sized orders (practice stealth trading), have large trading volume, are located in a financial center, trade early in the trading session, at times of wide spreads and when the order book is thin.     

Volatility,Depth, and Order Composition: Evidence from a Pure Limit Order Futures Market

This paper investigates market behaviors (such as volatility, depth, and volume) and order-flow decomposition in a pure limit order futures market, the Taiwan Futures Exchange. The results are different from those in equity markets due to relatively high adverse selection costs in futures markets. We show that a volatility (depth) increase is followed by a depth (volatility) decrease; a market order increase (decrease) subsequently induces higher (lower) volatility; and a limit order increase (decrease) results in more (less) market orders and limit orders. When the upside (downside) volatility rises, buyers decrease (increase) subsequent limit bid orders, and sellers increase (decrease) limit ask orders.