Related papers: A reduced-form model for level-1 limit order books
We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The most interesting features concern (i) the statistics of…
We develop an empirical behavioural order-driven (EBOD) model, which consists of an order placement process and an order cancellation process. Price limit rules are introduced in the definition of relative price. The order placement process…
In this paper we explore optimal liquidation in a market populated by a number of heterogeneous market makers that have limited inventory-carrying and risk-bearing capacity. We derive a reduced form model for the dynamic of their aggregated…
We propose a microscopic model to describe the dynamics of the fundamental events in the limit order book (LOB): order arrivals and cancellations. It is based on an operator algebra for individual orders and describes their effect on the…
In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an…
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 formulate a simplified model of a limit order book, in which the arrival process is independent of the current state. We prove a phase transition result: there exist prices $\kappa_b$ and $\kappa_a$ such that, for any $\epsilon > 0$,…
Modeling limit order books (LOBs) dynamics is a fundamental problem in market microstructure research. In particular, generating high-dimensional volume snapshots with strong temporal and liquidity-dependent patterns remains a challenging…
We use random walks to simulate the fluid limit of two coupled diffusive limit order books to model correlation emergence. The model implements the arrival, cancellation and diffusion of orders coupled by a pairs trader profiting from the…
We investigate present some new statistical properties of order books. We analyse data from the Nasdaq and investigate (a) the statistics of incoming limit order prices, (b) the shape of the average order book, and (c) the typical life time…
We propose a general non-linear order book model that is built from the individual behaviours of the agents. Our framework encompasses Markovian and Hawkes based models. Under mild assumptions, we prove original results on the ergodicity…
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…
This paper presents an equilibrium model of dynamic trading, learning, and pricing by strategic investors with trading targets and price impact. Since trading targets are private, rebalancers and liquidity providers filter the child order…
The existing literature provides evidence that limit order book data can be used to predict short-term price movements in stock markets. This paper proposes a new neural network architecture for predicting return jump arrivals in equity…
We study the optimal placement problem of a stock trader who wishes to clear his/her inventory by a predetermined time horizon t, by using a limit order or a market order. For a diffusive market, we characterize the optimal limit order…
In this paper we present a novel approach to the determination of fat tails in financial data by studying the information contained in the limit order book. In an order-driven market buyers and sellers may submit limit orders, which are…
We present a general framework for modelling the dynamics of limit order books, built on the combination of two modelling ingredients: the order flow, modelled as a general spatial point process, and market clearing, modelled via a…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
The tatonnement process in high frequency order driven markets is modeled as a search by buyers for sellers and vice-versa. We propose a total order book model, comprising limit orders and latent orders, in the absence of a market maker. A…
This study proposes a versatile model for the dynamics of the best bid and ask prices using an extended Hawkes process. The model incorporates the zero intensities of the spread-narrowing processes at the minimum bid-ask spread,…