THEORY OF RATIONAL OPTION PRICING
MAS61017 FINANCIAL MATHEMATICS PROJECT
SUBMISSION DEADLINE: 12 MID-DAY ON TUESDAY 30 JANUARY 2024
Project brief. The purpose of this project is to understand sections 1,2, 4
and8of[Merton 73](freelyavailablefromhttp://www.jstor.org/stable/3003143).
You should produce a written report explaining the main ideas you en-
counter. Specifically, your project should focus on
(a) the various equalities and inequalities satisfied by option prices,
(b) the derivation of the price of the perpetual American put option.
The report should aim to be a clear demonstration that you have obtained
a good understanding of the material. This will involve an account — in
your own words — of what you have read, giving sufficient detail on the
underlying material so as to make it as clear as possible. The report should
aim to be understandable by the other Financial Mathematics students who
have not undertaken the project.
Some of the material in (a) will be familiar from our lectures; you should
not devote too much of the report to this, unless the article provides you
with a novel way of understanding this material or you feel that you are
now able to demonstrate a deeper level of understanding than you achieved
before commencing the project.
You may benefit from reading other sources that contain relevant mate-
rial. All sources must be referenced using one of the University’s approved
referencing styles.
Your grade for the project will reflect how well you are able to learn this
new material independently and how well you can communicate it in your
own words. You may need to understand unexplained terminology from its
context and perhaps from other sources. A fuller description of the mark-
scheme will follow.
The project should be typed using LaTeX, Microsoft Word, or any other
appropriate typesetting software. The report should aim to be in the order
of 10 pages long (no shorter than 5 and no longer than 15).
You are encouraged to read and discuss the material with your fellow stu-
dents, but the writing of the project must be done strictly individually with
no collaboration or collusion.
1
The project is worth 30% of the final mark for MAS61017, and accounts
for the 5-credit difference between the Level 3 and Master’s-level versions of
the module. This means that you should expect the whole process — from
reading the brief to submitting the project — to constitute around 50 hours
of work.
Submission. You will submit the project via Turnitin on the Financial
Mathematics Blackboard page by 12 mid-day on Tuesday 30 January
2024. The submissions will automatically be checked for plagiarism, based
on Turnitin’s extensive database of websites and previously submitted work
that it will cross-reference to look for similarities, generating a “similarity
report” for each submission. I will review each similarity report, and follow
up cases that require further investigation.
The University’s standard penalties for late submission apply. If you expect
to have difficulties meeting the deadline, please contact me, and seek an
extension using the form on the student intranet pages.
Unfair means. The University’s policies on unfair means apply to this
project, as to all work at the University. Please make sure you are famil-
iar with the material on the University’s page on this. You must not use
ChatGPT or any other generative AI software, and your submission should
include a declaration that you have not done so.
Final comments.
• While reading published academic work can be daunting, you are
well-versedenoughinthismaterialnowtounderstandwhatisthere!
• Iwillhaveofficehoursat11–12onFriday8and15December(Weeks
11 & 12), and Friday 12, 19 and 26 January. If you would like to
meet online, please send me an email in advance. Please do ask for
help if you need it.
• Please do not email me with questions on the material directly, but
instead use the discussion board on Blackboard. I will look out for
questions and try to help explain things there.
Sam Marsh, December 2023
References
[Merton 73] Robert C. Merton. Theory of rational option pricing. The Bell Journal of
Economics and Management Science, Vol. 4, No. 1, Spring, 1973.
