Related papers: A simple model of a limit order book
This paper investigates the effects of a low bound price. To do so, a popular and empirically proven model (Stahl (89') \cite{Stahl89}) is used. The model is extended to include an exogenously given bound on prices sellers can offer,…
We consider a service system where agents are invited on-demand. Customers arrive exogenously as a Poisson process and join a customer queue upon arrival if no agent is available. Agents decide to accept or decline invitations after some…
We introduce a new model in order to describe the fluctuation of tick-by-tick financial time series. Our model, based on marked point process, allows us to incorporate in a unique process the duration of the transaction and the…
We have considered the model of the phase transition of the second order for the Coulomb frustrated 2D charged system. The coupling of the order parameter with the charge was considered as the local temperature. We have found that in such…
Large monetary expansions do not necessarily generate consumer-price inflation, challenging scalar views of "money supply." Here we propose that monetary function is phase-dependent: newly issued base money can occupy distinct functional…
We consider a novel queuing problem where the decision-maker must choose to accept or reject randomly arriving tasks into a no buffer queue which are processed by $N$ identical servers. Each task has a price, which is a positive real…
We extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. Here using random walks with Sibuya waiting times to include a time-dependent stochastic…
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…
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and resilience evolve randomly in time. Trading is allowed in both…
In this paper we introduce two new Hawkes processes, namely, compound and regime-switching compound Hawkes processes, to model the price processes in limit order books. We prove Law of Large Numbers and Functional Central Limit Theorems…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
The standard Hotelling model assumes that the stock of an exhaustible resource is known. We expand on the model by Arrow and Chang that introduced stochastic discoveries and for the first time completely solve such a model using impulse…
We study the price impact of order book events - limit orders, market orders and cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow…
Latent order book models have allowed for significant progress in our understanding of price formation in financial markets. In particular they are able to reproduce a number of stylized facts, such as the square-root impact law. An…
A phase transition of gas-liquid type with an upper critical point is examined which arises in a model of charges of one sign on compensating background (OCP). The phase transition parameters are dependent on the detailed assumptions about…
We introduce a practical, interactive simulator of the limit order book for large-tick assets, designed to produce realistic execution, costs, and P&L. The book state is projected onto a tractable representation based on spread and volume…
We consider a model for a one-sided limit order book proposed by Lakner et al. We show that it can be coupled with a branching random walk and use this coupling to answer a non-trivial question about the long-term behavior of the price. The…
This paper develops a unified explicit solution theory for optimal execution through sequential limit-order placement in a limit order book. Rather than controlling only the trading speed of a metaorder, we determine how individual limit…
We study an online market-making problem in which a learner sequentially posts bid and ask prices for a single asset while interacting with traders holding private valuations. Unlike existing online learning formulations that assume fully…
Research on limit order book markets has been rapidly growing and nowadays high-frequency full order book data is widely available for researchers and practitioners. However, it is common that research papers use the best level data only,…