Hawkes Processes in Finance: A Review with Simulations
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Date
2016-06
Authors
Simon, Graham
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
Hawkes processes are flexible robust models for simulating many self-exciting
features seen in empirical data. Using a Hawkes process creates clusters in modeled
data that are frequently seen in different natural environments. Some frequent areas of
use for Hawkes processes include the study of earthquakes, neural networks, social
media sharing, and financial trading data. This work builds an accessible framework for
the undergraduate study of Hawkes processes through building step-by-step from point
processes to Poisson processes and eventually Hawkes models. A literature review of
current research and utilizations for Hawkes processes is then done to demonstrate some
of the dramatic growth seen in this field of research. Point clusters, kernel estimation,
parameter estimation, and algorithms for implementation are also discussed with simple
simulations performed in Excel.
Description
57 pages. A thesis presented to the Department of Mathematics and the Clark Honors College of the University of Oregon in partial fulfillment of the requirements for degree of Bachelor of Science, Spring 2016.
Keywords
Mathematics, Applied mathematics, Financial mathematics, Point processes, Hawkes models, Poisson processes, Probability theory