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.     

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.     

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.     

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.     

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.     

The information content of a limit order book: The case of an FX market

In this paper we examine the question of whether knowledge of the information contained in a limit order book helps to provide economic value in a simple trading scheme. Given the greater information content of the order book, over simple price information, it might naturally be expected that the order book would dominate. Using Dollar Sterling tick data, we find that despite the in-sample statistical significance of variables describing the structure of the limit order book in explaining tick-by-tick returns, they do not consistently add significant economic value out-of-sample. We show this using a simple linear model to determine trading activity, as well as a model-free genetic algorithm based on price, order flow, and order book information. We also find that the profitability of all trading rules based on genetic algorithms dropped substantially in 2008 compared to 2003 data.     

Asset pricing with investor sentiment: On the use of investor group behavior to forecast ASEAN markets

A study of investor behavior, using four investor groups (local, foreign, institutional, and dealer's accounts) on the Stock Exchange of Thailand (SET). The daily net purchases of each group are used as leading indicators for sentiment. The sentiments are examined with relation to each other and market returns. Eight proven macroeconomic factors with known cross-sectional relationships and known to forecast with returns are examined as a benchmark for the newly proposed sentiment factor model. Retesting the factors allows for an apples to apples comparison with the proposed sentiment factors. Using a VAR framework this research finds that dealers predominantly sell to institutional accounts, creating a negative correlation between the two groups, in addition to strong institutional herding which is all indicative of potential agency problems on the exchange. Also find that local individual accounts practice negative feedback trading and the other groups practice positive feedback trading. Of the four groups, the only group that influences the SET is the local individual group of investors. The foreign investor is found to be the least significant group on market returns, provide market liquidity to locals, and be the least responsive to daily market changes-following the prudent man rule. Lastly, propose a simple model, using investor behavior to accurately predict the market's direction for the following day 76 percent of the time with market timing ability (66 percent in Malaysia). This can be useful for buying and shorting the market.     

Applying hedging strategies to estimate model risk and provision calculation

We present an empirical study of the intertwined behaviour of members in a financial market. Exploiting a database where the broker that initiates an order book event can be identified, we decompose the correlation and response functions into contributions coming from different market participants and study how their behaviour is interconnected. We find evidence for the following. (1) Brokers are very heterogeneous in liquidity provision—some appear to be primarily liquidity providers while others are primarily liquidity takers. (2) The behaviour of brokers is strongly conditioned on the actions of other brokers. In contrast, brokers are only weakly influenced by the impact of their own previous orders. (3) The total impact of market orders is the result of a subtle compensation between the same broker pushing the price in one direction and the liquidity provision of other brokers pushing it in the opposite direction. These results enforce the picture of market dynamics being the result of the competition between heterogeneous participants, interacting to form a complex market ecology.     

The impact of investor sentiment on crude oil market risks: evidence from the wavelet approach

Investor sentiment has become an important factor affecting oil price volatility and extreme risk. Therefore, we utilise a VaR-GARCH model to detect the extreme risk of the crude oil market during 2007–2017, and then explore the causality between investor sentiment and extreme risk in the crude oil market, and their lead-lag and co-movement relationships in the time-frequency domain. The empirical results show that: firstly, investor sentiment leads downside risk but lags the upside risk in the crude oil market; secondly, in the time domain, there is a co-movement between investor sentiment and extreme risk in the crude oil market, in particular, investor sentiment may Granger cause extreme risk in the crude oil market at the 1% significance level but not vice versa; thirdly, in the frequency domain, weak coherence can be found in high-frequency bands but increases in low-frequency bands during the whole sample period, which indicates that the impact of investor sentiment on extreme risk in the crude oil market will last for a long time, although the affected period tends to decrease.     

Scheduled macro-news effects on a Euro/US dollar limit order book around the 2008 financial crisis

Characteristics of a complete limit order book (LOB) for Euro/US dollar in 2006-09, are asymmetrically affected by scheduled macro news announcements during the financial crisis. Depth is the most responsive characteristic followed by spread, volatility and slope. Depth and volatility respond more to expansion surprises, while spread and slope are more sensitive to recession. The effect of the announcement’s occurrence without surprise is overwhelmingly positive (negative) for depth and volatility (spread) in both regimes. This effect is mitigated by the surprise. More than half of US scheduled news surprises have state dependent depth coefficients, most with opposing signs between recession and expansion. Using all quote levels generates stronger characteristic response, indicating the existence of information outside of the best quotes.     

Optimal execution strategies in limit order books with general shape functions

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005 Obizhaeva, A and Wang, J. 2005. Optimal trading strategy and supply/demand dynamics, Preprint Available online at: http://www.rhsmith.umd.edu/faculty/obizhaeva/OW060408.pdf (accessed 16 February 2009)[Crossref] , [Google Scholar]) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modelling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e. of the volume of the LOB, or the exponential recovery of the bid–ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy of a risk-neutral investor, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005 Obizhaeva, A and Wang, J. 2005. Optimal trading strategy and supply/demand dynamics, Preprint Available online at: http://www.rhsmith.umd.edu/faculty/obizhaeva/OW060408.pdf (accessed 16 February 2009)[Crossref] , [Google Scholar]). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.     

The pricing of sentiment risk in European stock markets

This paper studies whether sentiment is rewarded with a significant risk premium in the European stock markets. We examine several sentiment proxies and identify the Economic Sentiment Indicator from the EU Commission as the most relevant sentiment proxy for our sample. The analysis is performed for the contemporaneous excess returns of EA-11 stock markets in the period from February 1999 to September 2015. We apply a conditional multi-beta pricing model in order to track the variation of the sentiment risk premium over time. The results demonstrate a positive significant relationship between sentiment and contemporaneous excess returns which is consistent with previous studies. The calculated sentiment risk premium is significant as well but negative implying that an investment in EA-11 countries over the examined time period – that is bearing sentiment risk – would have been unattractive to the investors on average.     

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.     

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.     

Investor sentiment and calendar anomaly effects: A case study of the impact of Ramadan on Islamic Middle Eastern markets

The holy month of Ramadan is usually a time of celebration and renewal in Muslim countries. This paper examines whether or not this is reflected in positive calendar anomalies effects in Islamic Middle Eastern stock markets during the period 1992-2007. Strong evidence is found of significant and positive calendar effects in respect to the whole period of Ramadan in most countries and it is argued that this can be attributed to the generally positive investor mood, or sentiment. Although Ramadan is a time of celebration for Muslims it also can be a time of uncertainty and this appears to result in the impact of the festival not being uniformly positive throughout Ramadan. It is found that market returns in the first and last days of Ramadan show high levels of statistically significant year-on-year variation. It is argued that this can possibly be attributed to synchronization-related herding effects amplifying the impact of the mood swings associated with this period. The paper also finds that although the overall Ramadan effect is both positive and statistically significant for most countries, the associated gains were only large enough to outweigh transactions costs and provide the basis of a profitable trading strategy in one market.     

The submission of limit orders or market orders: The role of timing and information in the Reuters D2000-2 system

Recent work in the market microstructure literature suggests that the speed with which orders arrive in the market impacts traders' order submission decisions. In this study we use an asymmetric autoregressive conditional duration (ACD) model to empirically investigate the influence on the submission of limit and market orders of changes in the time between the past submissions of different types of orders, changes in the slope of the limit order book, and changes in price uncertainty. We find that the expected time between the arrivals of successive orders in the foreign exchange market depends on the previous type of order submitted and the slope on both sides of the order book. Price uncertainty (volatility) plays a secondary role after accounting for the impact of changes in the slope of the order book. Lastly, we find that there are fundamental changes in the level of information contained in the submission of orders at the opening and closing of markets.     

Predictability of stock markets with disequilibrium trading. A commentary paper

The paper focuses on the problem of predictability of stock market returns with disequilibrium trading. It is shown that the predictability of returns may be the consequence of quantity constraints appearing in the markets due to the imposition of administrative restrictions on trade. A relevant test of predictability for the Warsaw Stock Exchange (WSE) based on information referring to disequilibrium states occurrence is proposed. The empirical results of its application to the WSE on a sample containing session-to-session observations from the period January 1995 to December 1999 strongly support the hypothesis of predictability.     

A rational expectations equilibrium model of urban growth and land markets

This paper presents a simple model of urban spatial growth under uncertainty with an infinite time horizon. The rational expectations equilibrium path (REE path) of the urban land market is obtained in explicit form as a function of exogenously given stochastic processes of future population, transport and household income in the city. Spatial and temporal characteristics of asset prices along the REE path are examined in detail.