Stochastic Modeling of Order Book Dynamics

[Abstract] In this project the order book model proposed by Cont et al. [10] is used as a starting point to model order book dynamics. This model nicely combines three desirable properties from earlier studies: it is easy to calibrate, it reproduces statistical properties of the order book and it allows to make analytical computations in the order book. The model is studied, calibrated and tested on real-time data from the London Stock Exchange. Possible improvements to the model are discussed and tested. A method to compute probabilities in the model will be presented: recovering densities by inverting continued fraction representations of Laplace transforms. This is also implemented and evaluated. Preface This document presents an overview of my work at All Options in Amsterdam, where I carried out my thesis research. All Options is an option trading company established in 1998 and is a leading liquidity provider on all major European derivative markets. All Options' core business is trading options on listed nancial instruments. The foundation has the objective to stimulate cooperation between academics and people who actually work with derivatives. The motivation behind being that there remains a considerable gap between how specialists in the academic and practical worlds think and communicate. Discussions between academics and practitioners result in projects, as for example this thesis, that are of value to all concerned. The eventual result is relevant from an academic perspective, whilst at the same time oering a solution to problems encountered in everyday practice. After spending an In-house day at the old Amsterdam Stock Exchange where All Options is situated, I became very motivated to do an internship at this company, and see how every day life is working as a quant at the forefront of the nancial markets. Therefore I decided to apply for a research project at All Options. This report presents the results of this thesis research, and is the nal assessment to complete the Master Programme in Applied Mathematics at the Delft University of Technology. The goal of this project was to develop and test a model that computes probable behavior in the order book. I accomplished to do this in 6 months, and am proud to present my results and conclusions here. This report describes every step that I took in reaching my concussions, and is written for people who do have a certain basis in Mathematics. Acknowledgment First of all I would …