uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
A framework for the Modeling of Order Book Dynamics based on Event Sizes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2013 (English)Article in journal (Refereed) Submitted
Abstract [en]

We propose a modeling framework for the dynamics of a reduced form order book in event time and based on event sizes. Our framework for the order book is influenced by \cite{ContLarrard12}, but compared to \cite{ContLarrard12} we allow the best bid ask spread to be larger than one tick. Based on the modeling assumption that the best bid as well as the best ask price can only move by at most one tick (up or down), when an event occurs, we show that the dynamics of this simplified order book is completely described by a non-linear transformation of  two processes $(X,Y)$. A key challenge in the modeling is the empirical fact that the high frequency order flow is strongly autocorrelated, a fact we have to deal with in the modeling of $(X,Y)$. The core of our framework is a semi linear regression type model for $(X,Y)$, influenced by  more classical ARMA and AR models, and one key degree of freedom is the potentially non-linear basis functions used in  the regression. We use results from the theory of random iterative function systems to understand issues concerning stationarity and ergodicity in our models. We show how to rapidly calibrate the model by inverting block Toeplitz matrices in an efficient way. All components are worked through and explain in an application and the predictability of the model for order flows and price moves are analyzed in the context of a high frequency dataset.

Place, publisher, year, edition, pages
2013.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-214108OAI: oai:DiVA.org:uu-214108DiVA: diva2:684067
Funder
Riksbankens Jubileumsfond, P10-0113:1
Available from: 2014-01-07 Created: 2014-01-07 Last updated: 2016-08-12Bibliographically approved

Open Access in DiVA

No full text

Other links

arXiv

Authority records BETA

Nyström, Kaj

Search in DiVA

By author/editor
Nyström, Kaj
By organisation
Analysis and Applied Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 480 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf