arXiv research

Negative step sizes improve second-order methods for neural networks.

SGD's performance improves with critical batch size, minimizing SFO complexity.

Improved queue-reactive model considers order sizes for better market simulation.

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 result…

A novel Hawkes Process model captures order sizes in LOBs, improving fit quality and market impact studies.

Multivariate Hawkes processes analyze order dynamics in financial markets.

Faster convergence and handling larger mini-batches for deep neural networks.

Statistical properties of an order book and the effect they have on price dynamics were studied using the high-frequency NASDAQ Level II data. It was observed that the size distribution of marketable orders (transaction sizes) has power law tails with an exponent 1+mu_{market}=2.4 \pm 0.1. The distribution of limit ord…

We study the statistical regularities of opening call auction using the ultra-high-frequency data of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. The distribution of the relative price, defined as the relative difference between the order price in opening call auction and the closing price of last tr…

Improved robustness in optimization methods using second-order information.

Modified Newton step for online learning reduces matrix size for large datasets.

We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extra…

Study examines tick size changes' impact on Japanese stock market efficiency.

Optimistic method adapted for faster convex-concave min-max problems.

We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock Exchange. As a result, the limit price is broadly distributed around the best price acc…

Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyze it using simulation, dimensional analy…

A new model for predicting market order book dynamics using a buffer Hawkes process.

Improved method finds second-order stationary points privately with better efficiency.

New method accelerates neural network training with large batch sizes using second-order information and adversarial training.

This paper studies the Glosten Milgrom model whose risky asset value admits an arbitrary discrete distribution. Contrast to existing results on insider's models, the insider's optimal strategy in this model, if exists, is not of feedback type. Therefore a weak formulation of equilibrium is proposed. In this weak formul…

The study examines order flow in financial markets using fractional Lévy stable motion.

SP-NGD improves deep learning models' generalization with large mini-batch sizes.

Muon optimizes training efficiency by improving data retention at large batch sizes.

Two Hawkes models integrate queue sizes to model order flow and improve accuracy.

Enhances queue-reactive model for realistic limit order book simulation.

Method detects and predicts iceberg orders on CME.

This paper studies a limit order book (LOB) model, in which the order dynamics depend on both, the current best available prices and the current volume density functions. For the joint dynamics of the best bid price, the best ask price, and the standing volume densities on both sides of the LOB we derive a weak law of …

New method reduces ensemble size for linear bandits, achieving near optimal regret.

The trade size $ω$ has direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization $C$ is included a…

This work improves SGD convergence by adaptively adjusting batch sizes.

A tick size is the smallest increment of a security price. It is clear that at the shortest time scale on which individual orders are placed the tick size has a major role which affects where limit orders can be placed, the bid-ask spread, etc. This is the realm of market microstructure and there is a vast literature o…

Novel adaptive method reduces Hessian computation for large-scale ERM.

This paper investigates the scaling dependencies between measures of "activity" and of "size" for companies included in the FTSE 100. The "size" of companies is measured by the total market capitalization. The "activity" is measured with several quantities related to trades (transaction value per trade, transaction val…

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 …

A new method for faster optimization of noisy functions.

Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [2, 19]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large orders are broken up into pieces and executed incrementally. If the size of such lar…

Study shows market quality improves with larger orders, not smaller tick sizes or higher trading frequencies.

A new theorem shows market impact is proportional to the square root of order size.

NMC improves MCMC convergence by analyzing gradients to determine optimal proposal densities.

Stochastic second-order methods converge fast under interpolation conditions.

Study identifies key metrics for small and large tick assets in LOBs.

Using the classification of transitive groups we classify indecomposable quandles of size <36. This classification is available in Rig, a GAP package for computations related to racks and quandles. As an application, the list of all indecomposable quandles of size <36 not of type D is computed.

It is known that the impact of transactions on stock price (market impact) is a concave function of the size of the order, but there exists little quantitative theory that suggests why this is so. I develop a quantitative theory for the market impact of hidden orders (orders that reflect the true intention of buying an…

Fewer obstructions for small graphs in knotless embedding.

Exchange improves liquidity by using different bid and ask tick sizes.

Model for cross-border markets with limited transmission capacities.

Improved computational complexity in statistical models using second-order information.

Deep learning predicts fit for fashion e-commerce.