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Register a new userTick Size Reduction and Price Clustering in a FX Order Book
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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).
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We study the analytical properties of a one-side order book model in which the flows of limit and market orders are Poisson processes and the distribution of lifetimes of cancelled orders is exponential. Although simplistic, the model provides an analytical tractability that should not be overlooked. Using basic results for birth-and-death processes, we build an analytical formula for the shape (depth) of a continuous order book model which is both founded by market mechanisms and very close to empirically tested formulas. We relate this shape to the probability of execution of a limit order, highlighting a law of conservation of the flows of orders in an order book. We then extend our model by allowing random sizes of limit orders, hereby allowing to study the relationship between the size of the incoming limit orders and the shape of the order book. Our theoretical model shows that, for a given total volume of incoming limit orders, the less limit orders are submitted (i.e. the larger the average size of these limit orders), the deeper is the order book around the spread. This theoretical relationship is finally empirically tested on several stocks traded on the Paris stock exchange.
We introduce a microscopic model for the dynamics of the order book to study how the lack of liquidity influences price fluctuations. We use the average density of the stored orders (granularity $g$) as a proxy for liquidity. This leads to a Price Impact Surface which depends on both volume $omega$ and $g$. The dependence on the volume (averaged over the granularity) of the Price Impact Surface is found to be a concave power law function $<phi(omega,g)>_gsimomega^delta$ with $deltaapprox 0.59$. Instead the dependence on the granularity is $phi(omega,g|omega)sim g^alpha$ with $alphaapprox-1$, showing a divergence of price fluctuations in the limit $gto 0$. Moreover, even in intermediate situations of finite liquidity, this effect can be very large and it is a natural candidate for understanding the origin of large price fluctuations.
The recent surge in Deep Learning (DL) research of the past decade has successfully provided solutions to many difficult problems. The field of quantitative analysis has been slowly adapting the new methods to its problems, but due to problems such as the non-stationary nature of financial data, significant challenges must be overcome before DL is fully utilized. In this work a new method to construct stationary features, that allows DL models to be applied effectively, is proposed. These features are thoroughly tested on the task of predicting mid price movements of the Limit Order Book. Several DL models are evaluated, such as recurrent Long Short Term Memory (LSTM) networks and Convolutional Neural Networks (CNN). Finally a novel model that combines the ability of CNNs to extract useful features and the ability of LSTMs to analyze time series, is proposed and evaluated. The combined model is able to outperform the individual LSTM and CNN models in the prediction horizons that are tested.
We show that the statistics of spreads in real order books is characterized by an intrinsic asymmetry due to discreteness effects for even or odd values of the spread. An analysis of data from the NYSE order book points out that traders strategies contribute to this asymmetry. We also investigate this phenomenon in the framework of a microscopic model and, by introducing a non-uniform deposition mechanism for limit orders, we are able to quantitatively reproduce the asymmetry found in the experimental data. Simulations of our model also show a realistic dynamics with a sort of intermittent behavior characterized by long periods in which the order book is compact and liquid interrupted by volatile configurations. The order placement strategies produce a non-trivial behavior of the spread relaxation dynamics which is similar to the one observed in real markets.
Traders in a stock market exchange stock shares and form a stock trading network. Trades at different positions of the stock trading network may contain different information. We construct stock trading networks based on the limit order book data and classify traders into $k$ classes using the $k$-shell decomposition method. We investigate the influences of trading behaviors on the price impact by comparing a closed national market (A-shares) with an international market (B-shares), individuals and institutions, partially filled and filled trades, buyer-initiated and seller-initiated trades, and trades at different positions of a trading network. Institutional traders professionally use some trading strategies to reduce the price impact and individuals at the same positions in the trading network have a higher price impact than institutions. We also find that trades in the core have higher price impacts than those in the peripheral shell.
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