Optimal order placement in limit order markets

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by characteristics of the order flows and queue sizes in each limit order book, as well as the structure of transaction fees and rebates across exchanges. We propose a quantitative framework for studying this order placement problem by formulating it as a convex optimization problem. This formulation allows the study of how the optimal order placement decision depends on the interplay between the state of order books, the fee structure, order flow properties and the aversion to execution risk. In the case of a single exchange, we derive an explicit solution for the optimal split between limit and market orders. For the general case of order placement across multiple exchanges, we propose a stochastic algorithm that computes the optimal routing policy and study the sensitivity of the solution to various parameters. Our algorithm does not require an explicit statistical model of order flow but exploits data on recent order fills across exchanges in the numerical implementation of the algorithm to acquire this information through a supervised learning procedure.     

Public information arrival: Price discovery and liquidity in electronic limit order markets

How information is translated into market prices is still an open question. This paper studies the impact of newswire messages on intraday price discovery, liquidity, and trading intensity in an electronic limit order market. We take an objective ex ante measure of the tone of a message to study the impacts of positive, negative, and neutral messages on price discovery and trading activity. As expected, we find higher adverse selection costs around the arrival of newswire messages. Negative messages are associated with higher adverse selection costs than positive or neutral messages. Liquidity increases around positive and neutral messages and decreases around negative messages. Available order book depth as well as the trading intensity increases around all news. Our results suggest that market participants possess different information gathering and processing capabilities and that negative news messages are particularly informative and induce stronger market reactions.     

Informed traders and limit order markets

We consider a dynamic limit order market in which traders optimally choose whether to acquire information about the asset and the type of order to submit. We numerically solve for the equilibrium and demonstrate that the market is a “volatility multiplier”: prices are more volatile than the fundamental value of the asset. This effect increases when the fundamental value has high volatility and with asymmetric information across traders. Changes in the microstructure noise are negatively correlated with changes in the estimated fundamental value, implying that asset betas estimated from high-frequency data will be incorrect.     

The self-financing equation in limit order book markets

The goal of this paper is to present a mathematical framework for trading on a limit order book, including its associated transaction costs, and to propose continuous-time equations which generalise the self-financing relationships of frictionless markets. These equations naturally differentiate between trading via limit and via market orders, as they include a price impact or adverse selection constraint. We briefly mention several possible applications, including hedging European options with limit orders, to illustrate their impact and how they can be used to the benefit of low-frequency traders. Two appendices include empirical evidence for facts which are not universally recognised in the current literature on the subject.

     

Reduced form modeling of limit order markets

This paper proposes a parametric approach for stochastic modeling of limit order markets. The models are obtained by augmenting classical perfectly liquid market models with a few additional risk factors that describe liquidity properties of the order book. The resulting models are easy to calibrate and to analyse using standard techniques for multivariate stochastic processes. Despite their simplicity, the models are able to capture several properties that have been found in microstructural analysis of limit order markets. Calibration of a continuous-time three-factor model to Copenhagen Stock Exchange data exhibits, for example, mean reversion in liquidity as well as the so-called crowding out effect, which influences subsequent mid-price moves. Our dynamic models are also well suited for analysing market resilience after liquidity shocks.     

Price dynamics in foreign currency futures markets

Nested tests of Samuelson's submartingale and martingale models of price behavior in an efficient futures market find significant autocorrelation at low lags in daily changes of log prices for four of ten currency futures contracts satisfying the assumptions of the statistical tests. Negative serial correlation following large price changes is also found. The analysis controls for bias due to institutional limits on daily price movements. Simulated trading based on out-of-sample forecasts suggests the dependencies probably could be exploited by traders who are members of the futures exchange to earn net profits greatly exceeding buy and hold.     

A behavioural model of investor sentiment in limit order markets

By incorporating behavioural sentiment in a model of a limit order market, we show that behavioural sentiment not only helps to replicate most of the stylized facts in limit order markets simultaneously, but it also plays a unique role in explaining those stylized facts that cannot be explained by noise trading, such as fat tails in the return distribution, long memory in the trading volume, an increasing and non-linear relationship between trade imbalance and mid-price returns, as well as the diagonal effect, or event clustering, in order submission types. The results show that behavioural sentiment is an important driving force behind many of the well-documented stylized facts in limit order markets.     

Price dynamics in refined petroleum spot and futures markets

This article characterizes the spot and futures price dynamics of two important physical commodities, gasoline and heating oil. Using a non-linear error correction model with time-varying volatility, we demonstrate many new results. Specifically, the convergence of spot and futures prices is asymmetric, non-linear, and volatility inducing. Moreover, spreads between spot and futures prices explain virtually all spot return volatility innovations for these two commodities, and spot returns are more volatile when spot prices exceed futures prices than when the reverse is true. Furthermore, there are volatility spillovers from futures to spot markets (but not the reverse), futures volatility shocks are more persistent than spot volatility shocks, and the convergence of spot and futures prices is asymmetric and non-linear. These results have important implications. In particular, since the theory of storage implies that spreasd vary with fundamental supply and demand factors, the strong relation between spreads and volatility suggests that these fundamentals — rather than trading induced noise — are the primary determinants of spot price volatility. The volatility spillovers, differences in volatility persistence, and lead-lag relations are consistent with the view that the futures market is the primary locus of informed trading in refined petroleum product markets. Finally, our finding that error correction processes may be non-linear, asymmetric, and volatility inducing suggests that traditional approaches to the study of time series dynamics of variables that follow a common stochastic trend that ignore these complexities may be mis-specified.     

Price limit performance: evidence from transactions data and the limit order book

In recent years, organized stock exchanges with daily price limits adopted wider limits as narrower limits were criticized for jeopardizing market efficiency. This study examines the impact of a wide price limit on price discovery processes, using data from the Kuala Lumpur Stock Exchange. Specifically, examined is the impact of daily price limits on (i) information asymmetry; (ii) arrival rates of informed traders; and (iii) order imbalance. Using both trade-to-trade transaction data and the limit order book, we compile evidence that price limits do not improve information asymmetry, delays the arrival of informed traders, and exacerbates order imbalance. These results suggest that price limits on individual securities do not improve price discovery processes but impose serious costs even when the limit band is as wide as 30%.     

Non-constant rates and over-diffusive prices in a simple model of limit order markets

Abstract

Using simple particle models of limit order markets, we argue that the mid-term over-diffusive price behaviour is due to the variability of market order and limit order rates. Several rules for rate changes are considered. We obtain analytical results for bid-ask spread properties, Hurst plots and price increment correlation functions.     

Price discovery in currency markets

This paper examines the price discovery process in currency markets, basing its analysis on the pivotal distinction between the customer (end-user) market and the interdealer market. It first provides evidence that this price discovery process cannot be based on adverse selection between dealers and their customers, as postulated in standard models, because the spreads dealers quote to their customers are not positively related to a trade’s likely information content. The paper then highlights three factors familiar in the literature – fixed operating costs, market power, and strategic dealing – that may explain the cross-sectional variation in customers’ spreads. The paper finishes by proposing a price discovery process relevant to liquid two-tier markets and providing preliminary evidence that this process applies to currencies.     

Price discrimination in input markets

We analyze the short‐ and long‐run implications of third‐degree price discrimination in input markets. In contrast to the extant literature, which typically assumes that the supplier is an unconstrained monopolist, in our model input prices are constrained by the threat of demand‐side substitution. In our model, the more efficient buyer receives a discount. A ban on price discrimination thus benefits smaller but hurts more efficient, larger firms. It also stifles incentives to invest and innovate. With linear demand, a ban on price discrimination benefits consumers in the short run but reduces consumer surplus in the long run, which is once again the opposite of what is found without the threat of demand‐side substitution.     

Price limit bands,asymmetric volatility and stock market anomalies: Evidence from emerging markets

I investigate the effects of imposing different bands of price limits on stock returns and volatility in the Egyptian (EGX), Thai (SET) and Korean (KRX) stock exchanges. In addition, the paper examines whether the switch from narrow price limits (NPL) to wider price limits (WPL) structurally alters volatility and the day of the week anomaly. Using the extended EGARCH and PARCH asymmetric volatility models, I found that the switch from NPL to WPL structurally altered both asymmetric volatility and the day of the week anomaly in the EGX, SET and KRX. I argue that the price discovery mechanism is disrupted due to the switch as closing prices do not fully reflect all information arrived in the market when prices hit the limits and that is reflected on volatility and market efficiency.     

Price discovery in government bond markets

Price discovery in government bond markets is explored using Norwegian data including trades from both tiers of the market and dealer identities. The results show that while aggregate interdealer order flow explains one-fourth of daily yield changes, aggregate customer order flow has little explanatory power. Dealers are heterogeneously informed and appear to have different sources of information. While some dealers mainly rely on their customer trades, others appear to rely on skill in acquiring and interpreting other relevant information, suggesting that dealers play an independent role in the price discovery process.     

Price setting in forward-looking customer markets

If consumers form habits in individual goods, firms face a time-inconsistency problem. Low prices in the future help attract customers in the present. Firms, therefore, have an incentive to promise low prices in the future, but price gouge when the future arrives. In this setting, firms benefit from “committing to a sticky price.” If consumers have incomplete information about costs and demand, the firm-preferred equilibrium has the firm price at or below a “price cap.” The model therefore provides an explanation for the simultaneous existence of a rigid regular price and frequent “sales”.     

Quasi-centralized limit order books

A quasi-centralized limit order book (QCLOB) is a limit order book (LOB) in which financial institutions can only access the trading opportunities offered by counterparties with whom they possess sufficient bilateral credit. In this paper, we perform an empirical analysis of a recent, high-quality data set from a large electronic trading platform that utilizes QCLOBs to facilitate trade. We argue that the quote-relative framework often used to study other LOBs is not a sensible reference frame for QCLOBs, so we instead introduce an alternative, trade-relative framework, which we use to study the statistical properties of order flow and LOB state in our data. We also uncover an empirical universality: although the distributions that describe order flow and LOB state vary considerably across days, a simple, linear rescaling causes them to collapse onto a single curve. Motivated by this finding, we propose a semi-parametric model of order flow and LOB state for a single trading day. Our model provides similar performance to that of parametric curve-fitting techniques but is simpler to compute and faster to implement.     

Second order approximations for limit order books

In this paper, we derive a second order approximation for an infinite-dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator (e.g. the volume standing at the top of the book). We study the fluctuations of the price and volume process relative to their first order approximation given in ODE–PDE form under two different scaling regimes. In the first case, we suppose that price changes are really rare, yielding a constant first order approximation for the price. This leads to a measure-valued SDE driven by an infinite-dimensional Brownian motion in the second order approximation of the volume process. In the second case, we use a slower rescaling rate, which leads to a non-degenerate first order approximation and gives a PDE with random coefficients in the second order approximation for the volume process. Our results can be used to derive confidence intervals for models of optimal portfolio liquidation under market impact.     

Price clustering in foreign exchange spot markets

This paper documents the existence of price clustering in the foreign exchange spot market for the German mark, the Japanese yen, the United Kingdom pound, the French franc, the Italian lira, and the Swedish krona. The U.S. dollar exchange rate indicative quotes for these currencies tend to exhibit clustering around right-most digits that end in either a “zero” or a “five.” The tendency for exchange rates to cluster has increased with increases in trading volume and volatility. Moreover, the tendency for exchange rates to cluster differs across currencies.     

Modelling intensities of order flows in a limit order book

We propose a parametric model for the simulation of limit order books. We assume that limit orders, market orders and cancellations are submitted according to point processes with state-dependent intensities. We propose new functional forms for these intensities, as well as new models for the placement of limit orders and cancellations. For cancellations, we introduce the concept of ‘priority index’ to describe the selection of orders to be cancelled in the order book. Parameters of the model are estimated using likelihood maximization. We illustrate the performance of the model by providing extensive simulation results, with a comparison to empirical data and a standard Poisson reference.