Modeling market activity using 1D non-homogeneous Hawkes Processes

Abstract

This paper can be seen as a light introduction to the study of Hawkes pro-
cesses and their applicability in the realms of finance. In particular, this paper
is concerned on the topic of modeling market activity and elaborates on how
Hawkes processes are superior to non-homogeneous Poisson processes in this re-
gard. After some rudimentary theory on point processes it goes more in depth
into the above mentioned processes and their likelihood estimators. The rest of
the paper is dedicated to the actual modeling procedure, its necessary prepa-
rations and results, delving into the possible real-world interpretations of what
the modeling tells us.

Popular Abstract

Are there underlying patterns in stock-trading data? Does the mar-
ket behave differently during Mondays as opposed to, say, on Wednes-
days? Can the behaviour be explained by just considering factors
outside of what’s happening on the exchange; or is there inherent
self-exciting behaviour in the data?
These are some of the questions being explored in this thesis. What emerged
from these inquiries was in fact that: yes, behaviour is significantly different
on a week-day basis; yes, there are certainly a tangible self-exciting component
to the data; and (as the above answers imply) yes, stock-trading data is full of
patterns.
To get to the bottom of these questions, a specific type of point process was used
in the modeling procedure: namely, the Hawkes process. The data-set at hand
was stock-trades in Volvo B shares during 2003–2004. What the Hawkes process
is good at is catching self-exciting behaviour in the data. It has parameters that
control how much a trade impacts the intensity of the model and for how long
that impact stays in effect. ”What is self-exciting behaviour then?” you ask.
Well, one could say that it is what happens when past events—let’s say that
someone buys a lot of stocks—influences future events by making them more
likely; in our case: it triggers other people to also buy stocks that otherwise
might not have done so.
This might seem like common sense, and it might be just that; but at least the
models confirmed this! But how do they confirm this? Well, what a model is
can be explained as a mathematical function that with the help of its parameters
tries to emulate the real-world behaviour (i.e. the data) as close as possible. The
objective is to get close to the real data using as few parameters as possible.
What came as a bit of a surprise was the fact that we get a better result by taking
into account what day of the week it is rather than assuming each day behaves
similarly. What was discovered was that the intensity of trading over a trading-
day followed a slightly U-shaped curve; and this curve was different enough
for each week-day to warrant five times as many parameters as the next-best
model! This should probably be taken into account when doing predictions on
stock-market behaviour. Other than that, this thesis should mainly be seen as a
primer on the interesting subject of Hawkes processes; or self-exciting processes
in general.

• author: Andersson, Eskil
• supervisor: Magnus Wiktorsson
• organization: Mathematical Statistics
• course: FMS820 20172
• year: 2017
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• language: English
• id: 8931143
• date added to LUP: 2018-01-05 11:33:09
• date last changed: 2018-01-05 11:33:09