A quantitative model of trading and price formation in financial markets

We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of a market, such as the diffusion rate of prices, which is the standard measure of financial risk, and the spread and price impact functions, which are the main determinants of transaction cost. Guided by dimensional analysis, simulation, and mean field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.Comment: 5 pages, 4 figure

Order Submission: The Choice between Limit and Market Orders

Most financial markets allow investors to submit both limit and market orders, but it is not always clear what affects the choice of order type. The authors empirically investigate how the time between order submissions, changes in the state of the order book, and price uncertainty influence the rate of submission of limit and market orders. The authors measure the expected time (duration) between the submissions of orders of each type using an asymmetric autoregressive conditional duration model. They find that the execution of market orders, as well as changes in the level of price uncertainty and market depth, impact the submissions of both best limit orders and market orders. After correcting for these factors, the authors also find differences in behaviour around market openings, closings, and unexpected events that may be related to changes in information flows at these times. In general, traders use more market (limit) orders at times when execution risk for limit orders is highest or the risk of unexpected price movements is highest.Exchange rate; Financial institution; Market structure and pricing

A Mathematical Approach to Order Book Modeling

Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional continuous-time Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence towards it. We also prove, by means of the functional central limit theorem (FCLT), that the rescaled-centered price process converges to a Brownian motion. We illustrate the analysis with numerical simulation and comparison against market data

Time-Varying Arrival Rates of Informed and Uninformed Trades

In this paper we extend the model of Easley and O'Hara (1992) to allow the arrival rates of informed and uninformed trades to be time-varying and forecastable. We specify a generalized autoregressive bivariate process for the arrival rates of informed and uninformed trades and estimate the model on 16 actively traded stocks on the New York Stock Exchange over 15 years of transaction data. Our results show that uninformed trades are highly persistent. Uninformed order arrivals clump together, with high uninformed volume days likely to follow high uninformed volume days, and conversely. This behavior is consistent with the passive characterization of the uninformed found in the literature. But we do find an important difference in how the uninformed behave; they avoid trading when the informed are forecasted to be present. Informed trades also exhibit complex patterns, but these patterns are not consistent with the strategic behavior posited in the literature. The informed do not appear to hide in order flow, but instead they trade persistently. We also investigate the correlation between the arrival rates of trades and trade composition on market volatility, liquidity and depth. We find that although volatility increases with the forecasted arrival rates of total trades, it is relatively independent of the forecasted composition of the trade. We use the opening bid-ask spread as a measure of market liquidity. We find that as the number of trades increases over time, the relative proportion of informed trades decreases and hence, spreads become narrower and the market becomes more liquid. Finally, we compute the price impact curve of consecutive buy orders and report the half life of the price impact as a measure of market depth. We find a positive correlation between the half life and total trades indicating that the market is deeper in presence of more trades.Arrival rates; informed trades; uninformed trades; autoregressive process; market depth; liquidity; volatility.

Measuring market liquidity: An introductory survey

Asset liquidity in modern financial markets is a key but elusive concept. A market is often said to be liquid when the prevailing structure of transactions provides a prompt and secure link between the demand and supply of assets, thus delivering low costs of transaction. Providing a rigorous and empirically relevant definition of market liquidity has, however, provided to be a difficult task. This paper provides a critical review of the frameworks currently available for modelling and estimating the market liquidity of assets. We consider definitions that stress the role of the bid-ask spread and the estimation of its components that arise from alternative sources of market friction. In this case, intra-daily measures of liquidity appear relevant for capturing the core features of a market, and for their ability to describe the arrival of new information to market participants

Tick Size Reduction and Price Clustering in a FX Order Book

We investigate the statistical properties of the EBS order book for the EUR/USD and USD/JPY currency pairs and the impact of a ten-fold tick size reduction on its dynamics. A large fraction of limit orders are still placed right at or halfway between the old allowed prices. This generates price barriers where the best quotes lie for much of the time, which causes the emergence of distinct peaks in the average shape of the book at round distances. Furthermore, we argue that this clustering is mainly due to manual traders who remained set to the old price resolution. Automatic traders easily take price priority by submitting limit orders one tick ahead of clusters, as shown by the prominence of buy (sell) limit orders posted with rightmost digit one (nine).Comment: 17 pages, Minor revision