Order Book Dynamics Research Articles

Limit Order Book dynamics and order size modelling using Compound Hawkes Process

Hawkes Process has been used to model Limit Order Book (LOB) dynamics in several ways in the literature however the focus has been limited to capturing the inter-event times while the order size is usually assumed to be constant. We propose a novel methodology of using Compound Hawkes Process for the LOB where each event has an order size sampled from a calibrated distribution. The process is formulated in a novel way such that the spread of the process always remains positive. Further, we condition the model parameters on time of day to support empirical observations. We make use of an enhanced non-parametric method to calibrate the Hawkes kernels and allow for inhibitory cross-excitation kernels. We showcase the results and quality of fits for an equity stock’s LOB in the NASDAQ exchange and compare them against several baselines. Finally, we conduct a market impact study of the simulator and show the empirical observation of a concave market impact function is indeed replicated.

Investor demand in syndicated EFSF/ESM bond issuances

The European Financial Stability Facility (EFSF) and the European Stability Mechanism (ESM) were set up at the peak of the European sovereign debt crisis to issue bonds and lend to countries under current funding stress. This study analyses investor demand in syndicated bond issuances of EFSF and ESM from 2014 to 2020 on an unprecedented granularity level using a dataset of individual orders with statistical inference. Particularly, we investigate orderbook dynamics for three main aspects: first, we determine the main factors segmenting investor demand. Second, we analyse price dynamics in the transactions and their relation to investor demand. Third, we investigate whether any indications of orderbook inflation might explain the increased volatility in orderbook volume. We identify issuance tranche and tenor as the main determinants of investor demand that are largely anticipated in the notional. Further, we note that ESM is doing economical pricing, where the new issue premium tends to be lower in a market context with larger demand. Lastly, we find a mixture of an increasing number and an increasing volume of orders as drivers of large order books. This confirms that there are no indications of orderbook inflation tendencies in the analysed time period.

Equity auction dynamics: latent liquidity models with activity acceleration

Equity auctions display several distinctive characteristics in contrast to continuous trading. As the auction time approaches, the rate of events accelerates causing a substantial liquidity buildup around the indicative price. This, in turn, results in a reduced price impact and decreased volatility of the indicative price. In this study, we adapt the latent/revealed order book framework to the specifics of equity auctions. We provide precise measurements of the model parameters, including order submissions, cancelations, and diffusion rates. Our setup allows us to describe the full dynamics of the average order book during closing auctions in Euronext Paris. These findings support the relevance of the latent liquidity framework in describing limit order book dynamics. Lastly, we analyze the factors contributing to a sub-diffusive indicative price and demonstrate the absence of indicative price predictability.

Bid-ask spread dynamics: large upward jump with geometric catastrophes

We propose a simple continuous-time stochastic model for capturing the dynamics of a limit order book in the presence of liquidity fluctuations, manifested by gaps in filled price levels within the OB. Inspired by [D. Farmer, L. Gillemot, F. Lillo, S. Mike and A. Sen, Quant. Finance 4 (2004) 383–397.], we define a model for the dynamics of spread that incorporates liquidity fluctuations and undertake a comprehensive theoretical study of the model’s properties, providing rigorous proofs of several key asymptotic theorems. Furthermore, we show how large deviations manifest in the spread under this regime.

Ship order book forecasting by an ensemble deep parsimonious random vector functional link network

Efficient forecasting of ship order books holds immense significance in the maritime industry, enabling companies to optimize their operations, allocate resources effectively, and make informed decisions. However, volatile characteristics within historical order books pose challenges in achieving reliable, intelligent, and precise forecasts. This paper presents a novel ensemble deep random vector functional link (edRVFL) algorithm to anticipate future ship order book dynamics. The edRVFL leverages deep feature extraction and ensemble learning to enhance forecasting performance. To further elevate its capabilities, we introduce a discontinuous and parsimonious embedding strategy, which deviates from the conventional dense collection of continuous time steps used in vanilla edRVFL. This parsimonious embedding approach limits the model’s complexity and boosts its generalization ability. We extensively evaluate the proposed method using ship order book data, and comparative studies demonstrate its superiority over alternative approaches. Our proposed edRVFL offers a promising solution for accurate and efficient ship order book forecasting, making it a valuable asset in the maritime industry’s decision-making processes. The source codes utilized in this research are openly available on GitHub at the following link: https://github.com/crkkkaa/Ship-order-book-forecasting-by-an-ensemble-deep-parsimonious-random-vector-functional-link-network-.

Optimal Incentives in a Limit Order Book: A SPDE Control Approach

With the fragmentation of electronic markets, exchanges are now competing in order to attract trading activity on their platform. Consequently, they developed several regulatory tools to control liquidity provision/consumption on their liquidity pool. In this paper, we study the problem of an exchange using incentives in order to increase market liquidity. We model the limit order book as the solution of a stochastic partial differential equation (SPDE) as in [R. Cont and M. S. Müller, 2021, A stochastic partial differential equation model for limit order book dynamics, SIAM Journal on Financial Mathematics 12(2), 744–787]. The incentives proposed to the market participants are functions of the time and the distance of their limit order to the mid-price. We formulate the control problem of the exchange who wishes to modify the shape of the order book by increasing the volume at specific limits. Due to the particular nature of the SPDE control problem, we are able to characterize the solution with a classic Feynman–Kac representation theorem. Moreover, when studying the asymptotic behavior of the solution, a specific penalty function enables the exchange to obtain closed-form incentives at each limit of the order book. We study numerically the form of the incentives and their impact on the shape of the order book, and analyze the sensitivity of the incentives to the market parameters.

Limit Order Book Dynamics and Order Size Modelling Using Compound Hawkes Process

Limit Order Book Dynamics and Order Size Modelling Using Compound Hawkes Process

Thermodynamic Analysis of Financial Markets: Measuring Order Book Dynamics with Temperature and Entropy.

This study bridges finance and physics by applying thermodynamic concepts to model the limit order book (LOB) with high-frequency trading data on the Bitcoin spot. We derive the measures of Market Temperature and Market Entropy from the kinetic and potential energies in the LOB to provide a deeper understanding of order activities and market participant behavior. Market Temperature emerges as a robust indicator of market liquidity, correlating with liquidity measures such as Active Quote Volume, bid-ask spread and match volume. Market Entropy, on the other hand, quantifies the degree of disorder or randomness in the LOB, providing insights into the instantaneous volatility of price in the high-frequency trading market. Our empirical findings not only broaden the theoretical framework of econophysics but also enhance comprehensive understanding of the market microstructure and order book dynamics.

Order Book Dynamics with Liquidity Fluctuations: Asymptotic Analysis of Highly Competitive Regime

We introduce a class of Markov models to describe the bid–ask price dynamics in the presence of liquidity fluctuations. In a highly competitive regime, the spread evolution belongs to a class of Markov processes known as a population process with uniform catastrophes. Our mathematical analysis focuses on establishing the law of large numbers, the central limit theorem, and large deviations for this catastrophe-based model. Large deviation theory allows us to illustrate how huge deviations in the spread and prices can occur in the model. Moreover, our research highlights how these local trends and volatility are influenced by the typical values of the bid–ask spread. We calibrated the model parameters using available high-frequency data and conducted Monte Carlo numerical simulations to demonstrate its ability to reasonably replicate key phenomena in the presence of liquidity fluctuations.

Kernel Market Impact Analysis in China A-Share Markets

With transaction-level market data for stocks in China A-share markets, the authors construct individual stocks’ kernel functions of market impact and analyze their statistical properties. Attribution analysis of such kernel functions is also performed to understand how market microstructure variables such as bid–ask spread and liquidity distribution in order books can be used to classify different groups of kernel functions. The authors’ analysis shows that stocks in China A-share markets exhibit clear patterns of market impact curves, which is likely due to specific market structure regulations such as constant tick size across different stocks and stock-specific order book dynamics resulting from market participants’ behaviors. The authors also explore the application of kernel functions in forecasting price movement in close-to-reality trading simulators that consider market impact costs at individual trade level.

Investor demand in syndicated EFSF/ESM bond issuances.

The European Financial Stability Facility (EFSF) and the European Stability Mechanism (ESM) were set up at the peak of the European sovereign debt crisis to issue bonds and lend to countries under current funding stress. This study analyses investor demand in syndicated bond issuances of EFSF and ESM from 2014 to 2020 on an unprecedented granularity level using a dataset of individual orders with statistical inference. Particularly, we investigate orderbook dynamics for three main aspects: first, we determine the main factors segmenting investor demand. Second, we analyse price dynamics in the transactions and their relation to investor demand. Third, we investigate whether any indications of orderbook inflation might explain the increased volatility in orderbook volume. We identify issuance tranche and tenor as the main determinants of investor demand that are largely anticipated in the notional. Further, we note that ESM is doing economical pricing, where the new issue premium tends to be lower in a market context with larger demand. Lastly, we find a mixture of an increasing number and an increasing volume of orders as drivers of large order books. This confirms that there are no indications of orderbook inflation tendencies in the analysed time period.

A generative model of a limit order book using recurrent neural networks

In this work, a generative model based on recurrent neural networks for the complete dynamics of a limit order book is developed. The model captures the dynamics of the limit order book by decomposing the probability of each transition into a product of conditional probabilities of order type, price level, order size and time delay. Each such conditional probability is modelled by a recurrent neural network. Several evaluation metrics for generative models related to trading execution are introduced. Using these metrics, it is demonstrated that the generative model can be successfully trained to fit both synthetic and real data from the Nasdaq Stockholm exchange.

The Impact of Fractional Trading on Order Book Dynamics

The Impact of Fractional Trading on Order Book Dynamics

A Mathematical Framework for Modelling Order Book Dynamics

A Mathematical Framework for Modelling Order Book Dynamics

A Stochastic Partial Differential Equation Model for Limit Order Book Dynamics

We propose an analytically tractable class of models for the dynamics of a limit order book, described through a stochastic partial differential equation with multiplicative noise for the order book centered at the mid-price, along with stochastic dynamics for the mid-price which is consistent with the order flow dynamics. We provide conditions under which the model admits a finite-dimensional realization driven by a (low-dimensional) Markov process, leading to efficient methods for estimation and computation. We study two examples of parsimonious models in this class: a two-factor model and a model in which the order book depth is mean reverting. For each model we perform a detailed analysis of the role of different parameters, study the dynamics of the price, order book depth, volume, and order imbalance, provide an intuitive financial interpretation of the variables involved, and show how the model reproduces statistical properties of price changes, market depth, and order flow in limit order markets.

Analysis of order book dynamics in the Japanese stock market using the Queue-Reactive Hawkes process

Analysis of order book dynamics in the Japanese stock market using the Queue-Reactive Hawkes process

How do Extreme Price Movements End?

We test competing theories of liquidity dynamics during extreme price movements (EPMs). We find that liquidity providers strategically allow for price pressures and are compensated from correcting pricing errors. As a result, liquidity provision intensifies towards the end of a typical EPM. This goes counter to a widespread concern that market making constraints cause liquidity to deteriorate as EPMs develop. The prevailing limit order book dynamics during EPMs are in line with Weill’s (2007) socially beneficial equilibrium.

Order Book Dynamics of Fine Wine Exchange

AbstractIn this paper, we explore the order book dynamics on the Liv-ex fine wine exchange. More specifically, by using the order book data, we examine new buy and sell order submissions and cancellations and various factors that may have an effect on the intensity of the trade process on both sides of the market. Our findings indicate the existence of significant relationships between the expected number of bids, offers, or order withdrawals and wine producers, contract type, bottle format, case size, weekday, and age. In particular, the wine age positively affects the buy and sell order submissions, but only up to a certain point, after which the number of orders starts to decrease. (JEL Classifications: D40, G12, G14, L66)

Order Book Dynamics in the Presence of Liquidity Fluctuations

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

Lead-Lag and Evasiveness of Price Limits Across Venues Based on Synchronised Orderbook Observations

In this paper, we show that synchronised market data across different venues can be of great help to better understand orderbook dynamics. We introduce a new measure for main European trading destinations: the “limit evasiveness”. It characterises the propensity of a limit to be cancelled without being emptied to prevent participants from consuming the liquidity displayed on the first limit. We show that Primary limits are less evasive than Cboe-ChiX. Lastly, we highlight the “leading venues”, by observing which the most frequent venues are when a trade is done at a better price compared to all the previous orderbooks’ best limits observed before this new trade. We show that Cboe-ChiX is overrepresented in leading instances, thus providing better effective prices to participants. It thus seems that MTFs are faster to cancel as well as to create new limits than primary markets. All these analyses are conducted based on c. 580,000 Smart Order Router market data observations from May 2019 that register best limits across different venues existing at a given point in time.