Date on Master's Thesis/Doctoral Dissertation

8-2013

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Mathematics

Committee Chair

Gill, Ryan

Committee Co-Chair (if applicable)

Lee, Kiseop

Committee Member

Riedel, Thomas

Committee Member

Powers, Robert

Committee Member

Kantardzic, Mehmed

Abstract

An application of a mixture of Poisson distributions is proposed to model the discrete changes in stock price based on the minimum price movement known as `tick-size'. The parameters are estimated using the Expectation-Maximization (EM) algorithm with a constant mixing probability as well as mixing probabilities which depend on order size. The model is evaluated using simulations and real data. Both the simulated and real data show reasonable estimates. Several adjustments are made to the model implementation to improve the efficiency with user written codes for the Newton Raphson algorithm and also implementing one of the most recent versions of the EM algorithm (PEM). Both the improvements show an exponentially increasing efficiency to the implementation. Further a Clustered Signed model is proposed to use summarized data to reduce the amount of data to be used in the model implementation using the discrete order sizes and the signs of the discrete stock price changes. The clustered model provided a significant time efficiency. A parametric bootstrap procedure is also considered to assess the significance of the order size on the mixing probabilities. The results show that the use of a variable mixture probability, which depends on the order size, is more appropriate for the model. The methods are illustrated with data from simulations and real data from Federal Express.

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Mathematics Commons

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