A Mathematical Approach to Order Book Modelling - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2011

A Mathematical Approach to Order Book Modelling

Résumé

We present a mathematical study of the order book as a multidimensional continuous- time Markov chain where the order ow is modeled by independent Poisson processes. Our aim is to bridge the gap between the microscopic description of price formation (agent- based modeling), and the Stochastic Di erential Equations approach used classically to describe price evolution at macroscopic time scales. To do this, we rely on the theory of in nitesimal generators and Foster-Lyapunov stability criteria for Markov chains. We motivate our approach using an elementary example where the spread is kept constant (\perfect market making"). Then we compute the in nitesimal generator associated with the order book in a general setting, and link the price dynamics to the instantaneous state of the order book. In the last section, we prove that the order book is ergodic| in particular it has a stationary distribution|that it converges to its stationary state exponentially fast, and that the large-scale limit of the price process is a Brownian motion.
Fichier principal
Vignette du fichier
A_Mathematical_Approach_to_Order_Book_Modeling_II.pdf (845.13 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00621253 , version 1 (12-09-2011)
hal-00621253 , version 2 (12-11-2012)
hal-00621253 , version 3 (13-05-2013)

Identifiants

  • HAL Id : hal-00621253 , version 2

Citer

Frédéric Abergel, Aymen Jedidi. A Mathematical Approach to Order Book Modelling. 2011. ⟨hal-00621253v2⟩
415 Consultations
8427 Téléchargements

Partager

Gmail Facebook X LinkedIn More