Related papers: Ergodicity and diffusivity of Markovian order book…
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…
In this paper we investigate a dynamic pricing model for constant demand elasticity where customers have a probability distribution on the number of items they order. This is a generalization from standard models which restrict customers to…
In this article, we consider a continuous review (s, S) inventory system with failures of demand fulfillment (service) modeled as a Markov-modulated retrial queueing system. The inventory system features a single product that experiences…
Empirical data reveals that the liquidity flow into the order book (depositions, cancellations andmarket orders) is influenced by past price changes. In particular, we show that liquidity tends todecrease with the amplitude of past…
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…
This paper develops a model for the bid and ask prices of a European type asset by formulating a stochastic control problem. The state process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend…
This paper focuses on some simple models of limit order book dynamics which simulate market trading mechanisms. We start with a discrete time/space Markov process and then perform a re-scaling procedure leading to a deterministic dynamical…
The main purpose of this paper is to extend the information-based asset-pricing framework of Brody-Hughston-Macrina to a more general set-up. We include a wider class of models for market information and in contrast to the original paper,…
This paper consists of two parts. The first part is devoted to empirical analysis of consolidated order book (COB) for the index RTS futures. In the second part we consider Poissonian multi--agent model of the COB. By varying parameters of…
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 present a simple dynamic equilibrium model for an online exchange where both buyers and sellers arrive according to a exogenously defined stochastic process. The structure of this exchange is motivated by the limit order book mechanism…
We introduce and treat rigorously a new multi-agent model of the continuous double auction or in other words the order book (OB). It is designed to explain collective behaviour of the market when new information affecting the market…
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…
Modeling the impact of the order flow on asset prices is of primary importance to understand the behavior of financial markets. Part I of this paper reported the remarkable improvements in the description of the price dynamics which can be…
We extend the now classic structural credit modeling approach of Black and Cox to a class of "two-factor" models that unify equity securities such as options written on the stock price, and credit products like bonds and credit default…
Understanding the emergence of universal features such as the stylized facts in markets is a long-standing challenge that has drawn much attention from economists and physicists. Most existing models, such as stochastic volatility models,…
R. Cont and A. de Larrard (SIAM J. Finan. Math, 2013) introduced a tractable stochastic model for the dynamics of a limit order book, computing various quantities of interest such as the probability of a price increase or the diffusion…
We introduce a simple model for addressing the controversy in the study of financial systems, sometimes taken as brownian-like processes and other as critical systems with fluctuations of arbitrary magnitude. The model considers a…
We consider the following Markovian dynamic on point processes: at constant rate and with equal probability, either the rightmost atom of the current configuration is removed, or a new atom is added at a random distance from the rightmost…
In this work, we present a continuous-time large-population game for modeling market microstructure betweentwo consecutive trades. The proposed modeling framework is inspired by our previous work [23]. In this framework, the Limit Order…