Limit Order Research Articles

Assessing the nutritional status of Southern Brazilian Eucalyptus plantations by the CND method

Genus Eucalyptus can be grown in different soils worldwide, although it is not always ready to fulfill plants’ nutrient demands. Whenever such nutrient shortage happens, it is necessary applying the nutrients missing, which can be established based on the critical levels and sufficiency ranges (SRs) of nutrients in leaves or by multivariate mathematical models, such as the composition nutrient diagnosis (CND). This study aimed to investigate the nutritional status of Eucalyptus plantations in Brazil, based on the CND method. A total of 119 12-month-old Eucalyptus saligna (E. saligna) plantations were sampled in the Rio Grande do Sul State (RS), Southern Brazil. Nutrient concentration in leaves and the diameter at breast height (DBH) was measured. The E. saligna nutritional status was calculated through the CND method. High- and low-yield populations were set based on DBH of 4.2 cm. The SRs proposed by the CND method were narrower than the ones proposed by official recommendations for Eucalyptus, especially for magnesium (Mg), boron (B), and iron (Fe). The CND-r2 index recorded for each nutrient generated a limitation order for nutrients. The greater accuracy of the recommendations proposed by the CND method, compared with univariate and bivariate methods, contribute to reducing the use of fertilizers.

Improving reinforcement learning algorithms: Towards optimal learning rate policies

AbstractThis paper shows how to use results of statistical learning theory and stochastic algorithms to have a better understanding of the convergence of Reinforcement Learning (RL) once it is formulated as a fixed point problem. This can be used to propose improvement of RL learning rates. First, our analysis shows that the classical asymptotic convergence rate is pessimistic and can be replaced by with , and the number of iterations. Second, we propose a dynamic optimal policy for the choice of the learning rate used in RL. We decompose our policy into two interacting levels: the inner and outer levels. In the inner level, we present the PASS algorithm (for “PAst Sign Search”) which, based on a predefined sequence of learning rates, constructs a new sequence for which the error decreases faster. The convergence of PASS is proved and error bounds are established. In the outer level, we propose an optimal methodology for the selection of the predefined sequence. Third, we show empirically that our selection methodology of the learning rate outperforms significantly standard algorithms used in RL for the three following applications: the estimation of a drift, the optimal placement of limit orders, and the optimal execution of a large number of shares.

Statistical arbitrage trading across electricity markets using advantage actor–critic methods

In this paper, risk-constrained arbitrage trading strategies that exploit price differences arising across short-term electricity markets, namely day-ahead (DAM), continuous intraday (CID) and balancing (BAL) markets, are developed and evaluated. To open initial DAM positions, a rule-based trading policy using DAM and CID price forecasts is proposed. DAM prices are predicted using both technical indicator features and data augmentation methods, such as autoencoders and generative adversarial networks. Meanwhile, CID prices are predicted using novel features that are engineered from the limit order book. Using the forecasts, the direction of price movements is correctly predicted the majority of the time. To manage open DAM positions while optimising the risk-reward ratio, deep reinforcement learning agents trained using the advantage actor–critic algorithm (A2C) are employed. Evaluated across Dutch short-term markets, A2C yields profits surpassing those obtained using A3C and other benchmarks. We expect our study to benefit electricity traders and researchers who seek to develop state-of-art intelligent trading strategies.

Ultrasensitive Homogeneous Detection of PCSK9 and Efficacy Monitoring of the PCSK9 Inhibitor Based on Proximity Hybridization-Dependent Chemiluminescence Imaging Immunoassay.

Accurate quantification of proprotein convertase subtilisin/kexin type 9 (PCSK9) in serum before and after the medication is helpful in grasping the evolution of PCSK9-related disease and evaluating the efficacy of PCSK9 inhibitors. Conventional approaches for PCSK9 quantification suffered from complicated operations and low sensitivity. By integrating stimuli-responsive mesoporous silica nanoparticles, dual-recognition proximity hybridization, and T7 exonuclease-assisted recycling amplification, a novel homogeneous chemiluminescence (CL) imaging approach was proposed for ultrasensitive and convenient immunoassay of PCSK9. Owing to the intelligent design and signal amplification property, the whole assay was conducted without separation and rinsing, significantly simplifying the procedure and eliminating the errors associated with the professional operation; meanwhile, it showed linear ranges over 5 orders of magnitude and detection limit as low as 0.7 pg mL-1. Parallel testing was allowed due to the imaging readout, which brought a maximum throughput of 26 tests h-1. The proposed CL approach was applied to analyze PCSK9 from hyperlipidemia mice before and after the intervention of the PCSK9 inhibitor. Serum PCSK9 levels in the model group and the intervention group could be distinguished efficiently. The results were reliable compared to commercial immunoassay results and histopathologic findings. Thus, it could facilitate the monitoring of the serum PCSK9 level and the lipid-lowering effect of the PCSK9 inhibitor, showing promising potential in bioanalysis and pharmaceuticals.

Association Between Multidrug-Resistant Bacteria and Mortality in Critically Ill Patients.

Multidrug-resistant bacteria (MDRB) carriage may impact the outcomes of intensive care unit (ICU) patients. In this study, we aimed to assess the effect of MDRB-related infection and colonization on the day60 mortality rate. We conducted a retrospective, observational study in a single university hospital ICU. From January 2017 to December 2018, we screened all patients admitted to the ICU for at least 48h for MDRB carriage. The primary outcome was the mortality rate on day60 after MDRB-related infection. The secondary outcome was the mortality rate on day60 of non-infected but colonized patients with MDRB. We considered the effect of potential confounders, such as the occurrence of septic shock, inadequate antibiotic therapy, Charlson score, and life-sustaining limitation order. We included 719 patients during the aforementioned period; of this number, 281 (39%) had a microbiologically documented infection. MDRB was found in 40 (14%) patients. The crude mortality rate in the MDRB-related infection group was 35% vs. 32% in the non-MDRB-related infection group (p = 0.1). Logistic regression showed that MDRB-related infection was not associated with excess mortality, with an odds ratio of 0.52 and a 95% confidence interval from 0.17 to 1.39 (p = 0.2). Charlson score, septic shock, and life-sustaining limitation order were significantly associated with an increased mortality rate on day60. No effect of MDRB colonization on mortality rate on day60 was highlighted. MDRB-related infection or colonization was not associated with an increased mortality rate on day60. Other confounders, such as comorbidities, may account for a higher mortality rate.

Drude weights in one-dimensional systems with a single defect

Ballistic transport of a quantum system can be characterized by Drude weight, which quantifies the response of the system to a uniform electric field in the infinitely long timescale. The Drude weight is often discussed in terms of the Kohn formula, which gives the Drude weight by the derivative of the energy eigenvalue of a finite-size system with the periodic boundary condition in terms of the Aharonov-Bohm flux. Recently, the Kohn formula is generalized to nonlinear responses. However, the nonlinear Drude weight determined by the Kohn formula often diverges in the thermodynamic limit. In order to elucidate the issue, in this work we examine a simple example of a one-dimensional tight-binding model in the presence of a single defect at zero temperature. We find that its linear and non-linear Drude weights given by the Kohn formula (i) depend on the Aharonov-Bohm flux and (ii) diverge proportionally to a power of the system size. We argue that the problem can be attributed to different order of limits. The Drude weight according to the Kohn formula (``Kohn--Drude weight'') indicates the response of a finite-size system to an adiabatic insertion of the Aharonov-Bohm flux. While it is a well-defined physical quantity for a finite-size system, its thermodynamic limit does not always describe the ballistic transport of the bulk. The latter should be rather characterized by a ``bulk Drude weight'' defined by taking the thermodynamic limit first before the zero-frequency limit. While the potential issue of the order of limits has been sometimes discussed within the linear response, the discrepancy between the two limits is amplified in nonlinear Drude weights. We demonstrate the importance of the low-energy excitations of $O(1/L)$, which are excluded from the Kohn--Drude weight, in regularizing the bulk Drude weight.

A Time-Dependent Markovian Model of a Limit Order Book

This paper considers a Markovian model of a limit order book where time-dependent rates are allowed. With the objective of understanding the mechanisms through which a microscopic model of an orderbook can converge to more general diffusion than a Brownian motion with constant coefficient, a simple time-dependent model is proposed. The model considered here starts by describing the processes that govern the arrival of the different orders such as limit orders, market orders and cancellations. In this sense, this is a microscopic model rather than a ``mesoscopic'' model where the starting point is usually the point processes describing the times at which the price changes occur and aggregate in these all the information pertaining to the arrival of individual orders. Furthermore, several empirical studies are performed to shed some light into the validity of the modeling assumptions and to verify whether certain stocks satisfy the conditions for their price process to converge to a more complex diffusion.

Market conditions and order-type preference

This paper proposes a methodology to investigate the relative preference of limit orders when changes in market conditions lead to temporary violations of the zero-profit condition. We formulate this preference as a function of the intraday structural price components of information and liquidity, the time variation in which is driven by expectations of an expandable set of measures of time varying market conditions. This is then used to investigate when the equilibrium zero-profit condition might be violated, which would lead to a preference for a particular order type. The resulting theoretical and empirical predictions of advanced microstructural pricing models suggest that limit orders should be preferred during periods of intense market activity, such as periods of high volume and short duration, when the price components are positively correlated, and during periods of less intense activity when the components are negatively correlated.

Analysis and modeling of client order flow in limit order markets

Four distinct clusters of client order flow are identified and their properties analyzed

Celestial locality and the Jacobi identity

We show the equivalence of several different tests of the Jacobi identity for celestial currents at tree level, in particular finding a simple, practical condition on hard momentum space 4-point amplitudes in any EFT. Along the way we clarify the role of the order of soft and collinear limits in obstructing the Jacobi identity for soft insertions and we argue that, despite their current-algebra-like properties, soft insertions as formulated in this paper cannot be interpreted as local operators in celestial conformal field theory.

Spoilt for choice: Determinants of market shares in fragmented equity markets

We analyze the determinants of the trading volumes of different trading mechanisms in equity markets using an extensive panel data set from European markets comprising public limit order books, call auctions, dark pools, internalization platforms, and the over-the-counter market. Market shares, resulting from investors’ order routing decisions, are driven by the degree of immediacy and anonymity offered by the venues, their ability to offer off-tick executions, as well as the informational environment and conditions in the market. Findings for small and large trades are distinctly different, likely because traders jointly choose trade size and venue type.

Jump Diffusion Approximation for the Price Dynamics of a Fully State Dependent Limit Order Book Model

We study a microscopic limit order book model, in which the order dynamics depend on the current best bid and ask price and the current volume density functions, simultaneously, and derive its macroscopic high-frequency dynamics. As opposed to the existing literature on scaling limits for limit order book models, we include price changes which do not scale with the tick size in our model to account for large price movement, for example, being triggered by highly unforeseen events. Our main result states that, when the size of an individual limit order and the tick size tend to zero, while the order arrival rate tends to infinity, the microscopic limit order book model dynamics converge to two one dimensional jump diffusion processes describing the prices coupled with two infinite dimensional fluid processes describing the standing volumes at the buy and sell side.

Trader Competition in Fragmented Markets: Liquidity Supply Versus Picking-Off Risk

AbstractBy employing a dynamic model with two limit order books, we show that fragmentation is associated with reduced competition among liquidity suppliers and lower picking-off risk of limit orders. Due to these countervailing channels, the impact of fragmentation on liquidity and welfare differs with asset volatility: When volatility is high (low), liquidity and aggregate welfare in a fragmented market are higher (lower) than in a single market. However, fragmentation always shifts welfare away from agents with exogenous trading motives and toward intermediaries. We empirically corroborate our model’s predictions about liquidity. Our model reconciles the mixed results in the empirical literature.

“A posteriori” limited high order and robust schemes for transient simulations of fluid flows in gas dynamics

In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of our method is to allow an approximation with a high-order of accuracy in smooth regions of the flow, while ensuring robustness and a non-oscillatory behaviour in the regions of steep gradients, in particular across shocks.Following the Multidimensional Optimal Order Detection (MOOD) ([15,17]) approach, a candidate solution is computed at a next time level via a high-order accurate explicit scheme ([3,5]). A so-called detector determines if the candidate solution reveals any spurious oscillations or numerical issue and, if so, only the troubled cells are locally recomputed via a more dissipative scheme. This allows to design a family of “a posteriori” limited, robust and positivity preserving, as well as high accurate, non-oscillatory and effective scheme. Among the detecting criteria of the novel MOOD strategy, two different approaches from literature, based on the work of [15,17] and on [35], are investigated. Numerical examples in 1D and 2D, on structured and unstructured meshes, are proposed to assess the effective order of accuracy for smooth flows, the non-oscillatory behaviour on shocked flows, the robustness and positivity preservation on more extreme flows.

Cross-market spoofing

Since 2012, regulatory investigations have revealed widespread manipulation and collusive practices among banks active in over-the-counter (OTC) markets. These discoveries have resulted in fines and settlements amounting to billions of US dollars, criminal proceedings and stricter regulation worldwide. However, recent legal cases and regulatory reports indicate that authorities have stepped up their efforts to crack down on so-called “cross-market spoofing”. The manipulative tactic involves a combination of a genuine order in one market and a spoof order in another, which is notoriously difficult to detect. In this paper, we use a high-frequency data set of limit order book snapshots from the foreign exchange (FX) spot market to develop and test a methodology to assess the feasibility, and hence potential prevalence, of cross-market spoofing. Our findings show that predictable reactions follow potential single-market spoofs that a market manipulator may exploit. Crucially, we also find that predictability may be observed in closely related markets. In particular, we discover that EUR/JPY offers a reliable pathway for a manipulator to exploit via spoof orders at deeper levels in the EUR/USD or USD/JPY limit order books. The findings suggest that a manipulator is more likely to submit a spoof order in a liquid market and a resting order in a less liquid but closely related market, rather than vice versa. Moreover, cross-market spoof orders are more likely to be found in markets that act as hedging markets.

Optimal High-Frequency Trading in a Pro-Rata Microstructure with Predictive Information

We propose a framework to study optimal trading policies in a one-tick pro-rata limit order book, as typically arises in short-term interest rate futures contracts. The high-frequency trader has the choice to trade via market orders or limit orders, which are represented respectively by impulse controls and regular controls. We model and discuss the consequences of the two main features of this particular microstructure: first, the limit orders sent by the high frequency trader are only partially executed, and therefore she has no control on the executed quantity. For this purpose, cumulative executed volumes are modelled by compound Poisson processes. Second, the high frequency trader faces the overtrading risk, which is the risk of brutal variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. The optimal trading problem is studied by stochastic control and dynamic programming methods, which lead to a characterization of the value function in terms of an integro quasi-variational inequality. We then provide the associated numerical resolution procedure, and convergence of this computational scheme is proved. Next, we examine several situations where we can on one hand simplify the numerical procedure by reducing the number of state variables, and on the other hand focus on specific cases of practical interest. We examine both a market making problem and a best execution problem in the case where the mid-price process is a martingale. We also detail a high frequency trading strategy in the case where a (predictive) directional information on the mid-price is available. Each of the resulting strategies are illustrated by numerical tests.

A multifactor regime-switching model for inter-trade durations in the high-frequency limit order market

Modeling behaviors of inter-trade durations has been an important step to understand the market microstructure. Given that most existing models focused on intraday transaction data, we analyze limit order book (LOB) data in a high-frequency (HF) market and find that stocks’ inter-trade durations follow bimodal distributions peaking at levels of second and millisecond. To characterize this empirical property, we develop a multifactor regime-switching duration (MF-RSD) model, in which the modes of inter-trade durations are characterized as regimes and the transitions of regimes are determined by LOB-factor-dependent transition probability matrices. Using the model, we analyze the impact of LOB factors on inter-trade duration dynamics and find that the bimodal phenomenon is caused by the switchings of traders’ trading strategies between market making and price speculation. Our empirical studies show that the MF-RSD model not only produces good in-sample fit but also outperforms some benchmark models in out-of-sample predictions of inter-trade durations. • Inter-trade durations in high-frequency LOB exhibit a bimodal distribution. • A multifactor regime-switching model is built for inter-trade durations in HF. • The regimes of inter-trade durations are associated with the trader’s behaviors. • Our model has better out-of-sample performance compared with some benchmarks. • The summarized effects of LOB factors reveal principle of market microstructure.

Limit Order Book Simulation with Generative Adversarial Networks

Limit Order Book Simulation with Generative Adversarial Networks

Multivariate Hawkes-based Models in Limit Order Book: European, Spread and Basket Option Pricing

Multivariate Hawkes-based Models in Limit Order Book: European, Spread and Basket Option Pricing

Continuous-time modeling of financial returns based on Limit Order Book data

The Limit Order Book (LOB) of a financial security contains the list of buy and sell orders placed by traders on a single or across many exchanges for a given stock. As such, the amount of information contained in the LOB is much richer than that contained in the time history of the mean price, so it can potentially be exploited to model and predict more accurately the future returns. As far as we are aware, this work offers - for the first time - a dynamical systems perspective on the latter modeling problem, leading to a two-fold contribution: (i) we will define a new regressor, called Base Imbalance, and we will show that its predictive potential is more significant than the ones usually employed in the literature; (ii) we will discuss that the most suitable way to derive a model of the LOB dynamics is via continuous-time system identification, due to the event-based nature of the phenomenon at hand. The effectiveness of the proposed modeling strategy to be used in trading policies will be illustrated by means of a benchmark experimental data.