Skip to Main content Skip to Navigation
Theses

Stochastic order book modelling

Abstract : This thesis presents some aspects of stochastic order book modelling. In the first part, we analyze a model in which order arrivals are independent Poisson. We show that the order book is stable (in the sense of Markov chains) and that it converges to its stationary state exponentially fast. We deduce that the price generated in this setting converges to a Brownian motion at large time scales. We illustrate the results numerically and compare them to market data. In the second part, we generalize the results to a setting in which arrival times are governed by self and mutually existing processes. The last part is more applied and deals with the identification of a realistic multivariate model from the order flow. We describe two approaches: the first based on maximum likelihood estimation and the second on the covariance density function, and obtain a remarkable agreement with the data. We apply the estimated model to two specific algorithmic trading problems, namely the measurement of the execution probability of a limit order and its cost.
Complete list of metadata

Cited literature [39 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00997433
Contributor : ABES STAR :  Contact
Submitted on : Wednesday, May 28, 2014 - 10:39:08 AM
Last modification on : Thursday, October 8, 2020 - 3:25:29 AM
Long-term archiving on: : Thursday, August 28, 2014 - 11:26:52 AM

File

Thesis-AJ1.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-00997433, version 1

Collections

Citation

Aymen Jedidi. Stochastic order book modelling. Other. Ecole Centrale Paris, 2014. English. ⟨NNT : 2014ECAP0001⟩. ⟨tel-00997433⟩

Share

Metrics

Record views

400

Files downloads

616