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Empirical evaluation of a Markovian model in a limit order market
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2012 (English)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

A stochastic model for the dynamics of a limit order book is evaluated and tested on empirical data. Arrival of limit, market and cancellation orders are described in terms of a Markovian queuing system with exponentially distributed occurrences. In this model, several key quantities can be analytically calculated, such as the distribution of times between price moves, price volatility and the probability of an upward price move, all conditional on the state of the order book. We show that the exponential distribution poorly fits the occurrences of order book events and further show that little resemblance exists between the analytical formulas in this model and the empirical data. The log-normal and Weibull distribution are suggested as replacements as they appear to fit the empirical data better.

Place, publisher, year, edition, pages
2012. , 43 p.
Series
UPTEC F, ISSN 1401-5757 ; 12019
Keyword [en]
Markovian model, limit order book, limit order market, stock, stock market, price dynamics, log-normal, distribution, exponential, Weibull, Markovian queuing system, empirical data, financial assets, trading, trader, high, frequency, trading, order book, order flow, HFT, Joint probability density function, bid queue, ask queue
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-176726OAI: oai:DiVA.org:uu-176726DiVA: diva2:536914
Educational program
Master Programme in Engineering Physics
Presentation
2012-06-15, Å2004, Ångströmlaboratoriet, Lägerhyddsv. 1, Uppsala, 08:00 (English)
Uppsok
Technology
Supervisors
Examiners
Available from: 2012-07-05 Created: 2012-06-25 Last updated: 2012-07-05Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • 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