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.     

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.     

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 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 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”.     

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.     

Correlation dynamics in European equity markets

We examine correlation dynamics using daily data from 1993 to 2002 on the five largest Euro-zone stock market indices. We also study, for comparison, the correlations of a sample of individual stocks. We employ both unconditional and conditional estimation methodologies, including estimation of the conditional correlations using the symmetric and asymmetric DCC-MVGARCH model, extended with the inclusion of a deterministic time trend. We confirm the presence of a structural break in market index correlations reported by previous researchers and, using an innovative likelihood-based search, we find that the it occurred at the beginning the process of monetary integration in the Euro-zone. We find mixed evidence of asymmetric correlation reactions to news of the type modelled by conventional asymmetric DCC-MVGARCH specifications.     

High-frequency trading in a limit order book

Abstract

We examine two performance measures advocated for asymmetric return distributions: the Sortino ratio—originally introduced by Sortino and Price (Sortino F and Price L 1994 J. Investing 59–65)—and a measure based on power utility introduced in Leland (Leland H 1999 Financial Analysts J. 27–36). In particular, we investigate the role of the maximum principle in this context, and assess the conditions under which the measures satisfy it. Our results add further motivation for the use of a modified Sortino ratio, by placing it on a sound theoretical foundation. In this light, we discuss its relative merits compared with alternative approaches.     

Monitoring and limit order submission risks

This paper presents a formal analysis of the relation between monitoring and limit order submission risk. With heterogeneous information, limit order traders face two types of risk. First, they may be “picked off” when prices change unexpectedly after the limit order is entered (known as free trading option risk). Second, they face the possibility that their limit order will not result in a trade. To mitigate these risks, traders can monitor information and prices and cancel or revise their orders as needed. But such monitoring is costly, resulting in a trade-off between the cost of monitoring and the risks of limit order submission. The model predicts that if the stock is actively traded, limit order submission risks and order cancellations/revisions are positively related. Further, shares with a wide bid-ask spread will tend to have a lower rate of order cancellations and revisions than shares with small bid-ask spreads. Finally, the model suggests that if larger capitalization stocks have lower costs of gathering information (and hence more intense monitoring of limit orders), there will be more cancellations and revisions in limit orders. A sample of 23 liquid stocks provides evidence that is consistent with these three main hypotheses.     

Algorithmic trading in a microstructural limit order book model

We propose a microstructural modeling framework for studying optimal market-making policies in a FIFO (first in first out) limit order book (order book). In this context, the limit orders, market orders, and cancel orders arrivals in the order book are modeled as point processes with intensities that only depend on the state of the order book. These are high-dimensional models which are realistic from a micro-structure point of view and have been recently developed in the literature. In this context, we consider a market maker who stands ready to buy and sell stock on a regular and continuous basis at a publicly quoted price, and identifies the strategies that maximize their P&L penalized by their inventory. An extension of the methodology is proposed to solve market-making problems where the orders arrivals are modeled using Hawkes processes with exponential kernel.

We apply the theory of Markov Decision Processes and dynamic programming method to characterize analytically the solutions to our optimal market-making problem. The second part of the paper deals with the numerical aspect of the high-dimensional trading problem. We use a control randomization method combined with quantization method to compute the optimal strategies. Several computational tests are performed on simulated data to illustrate the efficiency of the computed optimal strategy. In particular, we simulated an order book with constant/ symmetric/ asymmetrical/ state dependent intensities, and compared the computed optimal strategy with naive strategies. Some codes are available on https://github.com/comeh.     

Correlation and return dispersion dynamics in Chinese markets

This paper studies the relation between firm-level return dispersions and correlations among Chinese stocks during periods of unusually large upward and downward swings. We analyze individual stock returns across 18 sectors and test if return dispersions and stock correlations show asymmetric patterns for extreme up and down markets. Evidence from studies on U.S. stocks suggests that equity return correlations tend to be much greater on the downside than on the upside and that the degree of comovement gets even stronger during extreme market states. However, in the case of Chinese stock market, we find that higher downside correlations apply to only stocks within the Financial sector. With the exception of Financial stocks, we find that stock correlations are significantly higher during up markets, rather than down markets. Regarding firm-level return dispersions, our findings are consistent with rational asset pricing model predictions. We find that equity return dispersions are significantly higher during periods of large price changes.     

Price dynamics in corn cash and futures markets: cointegration,causality, and forecasting through a rolling window approach

Financial Markets and Portfolio Management - This paper examines the causal structure among the daily corn futures and seven cash price series from Midwestern states from January 3, 2006, to March...     

Price formation and the appraisal function in real estate markets

A real estate market model characterized by incomplete information, costly search, and varying expectations is presented. The model describes a self-selection process for market participants and a distribution of transaction prices. These transaction prices, which arise from a Nash equilibrium, can be expressed as a noisy signal, reflecting incomplete information as well as the conditions of sale. The appraiser's role is formalized as the task of signal extraction. The model emphasizes the differences in information available to individual buyers and sellers, who make transactions only infrequently, and the appraiser, whose expertise comes from observing many transactions. Based on the model, it is shown that contrary to popular perceptions, appraisal smoothing is consistent with an optimal updating strategy.     

Modelling the shape of the limit order book

This article develops a parsimonious way to use the shape of the limit order book to produce an estimate of the asset price. The posited model captures and describes the evolution of the distribution of limit orders on the bid and ask sides of the LOB during the trading session and provides estimates of the execution asset price over time. The performance of the model is evaluated against some existing standards from the market microstructure literature during the trading session. Empirical evidence on listed companies confirm a strong contribution of our methodology to the innovation in asset prices, according to the information share coefficients. We also document a significant improvement relative to the Hasbrouck [J. Finance, 1991, 46, 179–207] model when our model estimates are included as regressors.     

Price limit changes,order decisions,and stock price movements: an empirical analysis of the Taiwan Stock Exchange

Review of Quantitative Finance and Accounting - This study examines the relationships among price limit changes, order submission decisions, and stock returns in the Taiwan Stock Exchange....     

Liquidity dynamics across public and private markets

In this paper we investigate cross-asset liquidity between equity markets and REITs and between REITs and private real estate markets. While many studies have investigated REIT liquidity, and there is an emerging interest in liquidity in the private real estate markets, there appears to be little knowledge of the dynamics of cross-market liquidity. We find lower levels of liquidity for REITs compared to a set of control firms matched on size and book-to-market ratios. Commonality in liquidity is also lower for REITs than the controls and the overall market. However, we do find an important difference in share turnover for REITs, which appears to have a higher level of commonality than found in other studies. We suggest that this may be due to the financial crisis. Additionally we find evidence of similar time-series variation in liquidity for public and private real estate markets. We also find significant directional causality for most liquidity proxies from the public to private real estate markets. Finally our results show that there is strong contemporaneous correlation between both public and private real estate market liquidity and the term spread and real investment and consumption spending. REIT liquidity measures based on intraday data also appear to contain important information not found in measures constructed from daily returns.