Related papers: General Compound Hawkes Processes in Limit Order B…
Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this…
This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…
I present an overview of some recent advancements on the empirical analysis and theoretical modeling of the process of price formation in financial markets as the result of the arrival of orders in a limit order book exchange. After…
Market information events are generated intermittently and disseminated at high speeds in real-time. Market participants consume this high-frequency data to build limit order books, representing the current bids and offers for a given…
We establish a first and second-order approximation for an infinite dimensional limit order book model (LOB) in a single (''critical'') scaling regime where market and limit orders arrive at a common time scale. With our choice of scaling…
The general model of coagulation is considered. For basic classes of unbounded coagulation kernels the central limit theorem (CLT) is obtained for the fluctuations around the dynamic law of large numbers (LLN). A rather precise rate of…
A micro-scale model is proposed for the evolution of the limit order book. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of bid…
In this paper, we attempt to detect an inflection or change-point resulting from the Covid-19 pandemic on supply chain data received from a large furniture company. To accomplish this, we utilize a modified CUSUM (Cumulative Sum) procedure…
We establish the weak convergence of the intensity of a nearly-unstable Hawkes process with heavy-tailed kernel. Our result is used to derive a scaling limit for a financial market model where orders to buy or sell an asset arrive according…
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…
We study the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. Our main assumption is that the point processes are constructed by biorthogonal…
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…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
In this paper, we establish general scaling limits for nearly unstable Hawkes processes in a mean-field regime by extending the method introduced by Jaisson and Rosenbaum. Under a mild asymptotic criticality condition on the self-exciting…
There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…
We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical…
We propose a model for the dynamics of a limit order book in a liquid market where buy and sell orders are submitted at high frequency. We derive a functional central limit theorem for the joint dynamics of the bid and ask queues and show…
We consider a sequence of Hawkes processes whose excitation measures may depend on the generation, and study its scaling limits in the near-unstable limiting regime. The limiting random measures, characterized via a nonlinear convolutional…
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging…
This study explores the prediction of high-frequency price changes using deep learning models. Although state-of-the-art methods perform well, their complexity impedes the understanding of successful predictions. We found that an…