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.     

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.     

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.     

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.     

期货市场交易结构、价格形成机制及其效率研究

做市商机制和连续竞价机制是现代期货市场主流的两类交易机制，连续竞价机制则成本较低，价格信号反应灵敏；做市商机制透明、公正，市场连续性较好，代表着期货市场交易机制的未来发展方向。通过对期货市场微观交易结构及价格形成机制的模型研究，结合我国的实际情况，比较考察了几种典型的期货交易机制在不同交易结构下的价格形成效率，对我国期货市场转型完善时期具有现实意义。     

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.     

A careful re-examination of seasonality in international stock markets: Comment on sentiment and stock returns

In questioning Kamstra, Kramer, and Levi’s (2003) finding of an economically and statistically significant seasonal affective disorder (SAD) effect, Kelly and Meschke (2010) make errors of commission and omission. They misrepresent their empirical results, claiming that the SAD effect arises due to a “mechanically induced” effect that is non-existent, labeling the SAD effect a “turn-of-year” effect (when in fact their models and ours separately control for turn-of-year effects), and ignoring coefficient-estimate patterns that strongly support the SAD effect. Our analysis of their data shows, even using their low-power statistical tests, there is significant international evidence supporting the SAD effect. Employing modern, panel/time-series statistical methods strengthens the case dramatically. Additionally, Kelly and Meschke represent the finance, psychology, and medical literatures in misleading ways, describing some findings as opposite to those reported by the researchers themselves, and choosing selective quotes that could easily lead readers to a distorted understanding of these findings.     

Liquidity Provision of Limit Order Trading in the Futures Market Under Bull and Bear Markets

Abstract:  This study investigates how limit orders affect liquidity in a purely order-driven futures market. Additionally, the possible asymmetric relationship between market depth and transitory volatility in bull and bear markets and the effect of institutional trading on liquidity provision behavior are examined as well. The empirical results demonstrate that subsequent market depth increases as transient volatility increases in bull markets. Market depth exhibits significantly positive relationship to subsequent transient volatility in bull markets. Additionally, although trading volume positively influences transient volatility in bull markets, no such relationship exists in bear markets. Liquidity provision decreases when institutional trading activity intensifies during bear markets. Thus, liquidity provision for limit orders differs between bull and bear markets.     

Price discovery in foreign exchange markets: A comparison of indicative and actual transaction prices

In this paper, we compare four months of Reuters EFX high frequency indicative data with D2000-1 inter-dealer transaction data for DEM/USD and GBP/USD. Contrary to previous studies, we find, using various information measures, that the matched tick-by-tick indicative data bear no qualitative difference from the transaction data, and have higher information content. Expanding the system to include order flow, due to its growing importance in exchange rate theory, we find that indicative data has a similar impact on order flow as transaction data. However, order flow has no impact on either price.     

Market structure and rating strategies in credit rating markets – A dynamic model with matching of heterogeneous bond issuers and rating agencies

This paper investigates the impact of rating agencies in a market with asymmetric information. In particular, the role of credit rating agencies as an intermediary between investors and bond issuers is discussed. We model this setting in a dynamic framework in which both rating agencies and bond issuers are of heterogeneous quality. Rating agencies can apply costly research technology to reveal the fundamental nature of bond issuers and engage in rating smoothing. We show that rating smoothing can compensate for low research quality, even though it is accompanied by a quality deterioration in the rating market and market clustering. Moreover, low-quality bond issuers have a general tendency to match with low-quality rating agencies. If investors place a strong emphasis on the reputation of rating agencies, rating markets also tend to be strongly clustered.     

A model of medium term exchange rate forecast in an open economy The case of the mexican peso

Keynes (1930) and Samuelson (1965) proposals open the possibility of matching predictability and efficiency, as evidenced by the seminal study by Fisher (1930). Recent findings suggest that the foreign exchange market gradually incorporates relevant information allowing the formation of prices in a rational manner but not randomly. Models of exchange rate by term based on asset valuation suggest that the inclusion of risk in the spot rate increases the degree of predictability. The results show that after incorporating an accurate measure of risk, predictability of medium term foreign exchange rate increases.