Independent Study Module III: Mathematical Finance
In Epiphany term, the Independent Study Module III (Math 3161) is
given by Iain MacPhee. My contact details are:
| Room |
CM303 (Mathematics Building 3rd floor) |
| E-mail |
i.m.macphee@durham.ac.uk |
| telephone |
(0191) 334 3106 |
| Office hour |
Thursday 11am |
The subject of this Independent Study Module is Mathematical
Finance, particularly pricing of options. The aim of this module is to
develop student self-sufficiency by enabling you to learn for yourself
some topics from Mathematical Finance. There are no lectures but there
is an office hour during which you are welcome to ask questions about
the material.
The topics you need to know by the end of the academic year are all
covered in the book "An Introduction to Mathematical Finance" by
S.M. Ross (ISBN 0-521-81429-4, second edition) and the first chapter
of the book "Options, Futures, & Other Derivatives" by J.C. Hull (ISBN
0-13-015822-4). Chapter 10 of Ross however is not exam material as
most of this material will be dealt with in the course Operational
Research. Chapters 1 and 2 are covered in year 1 and assumed to be
known. If you have problems with it, go back to your first year
probability notes or have a look in the book 'Elementary Probability'
by Stirzaker.
Advisory work schedule
The following work schedule is arranged so that every time homework is
set you have covered the material needed to do the homework. It is
much better to stick to a steady work schedule than leave all the work
to the last moment. As in term 1 there will be quite a few
exercises. This is because Mathematical Finance requires some
reasoning that you will not meet in your other mathematics courses and
the only way to get feeling for this kind of reasoning is by
practising. You don't have to follow this advisable work schedule and
you don't have to do the exercises. It is only to help you to divide
the material equally over the year and to prevent you from leaving
everything to the last moment. The idea is that you try to do the
exercises and communicate with other students about it. If you are
really lost, you should come and see me during the office hour with your
problem clearly formulated. The material and exercises refer to the
book of Ross unless stated otherwise.
| Week |
Material |
Exercises |
| 11 |
Sections 8.1, 8.2 |
8.2, 8.3 |
| 12 |
Section 8.3 |
8.5, 8.6 |
| 13 |
Sections 8.4, 8.5 |
8.7, 8.8, 8.12 |
| 14 |
Sections 8.6, 8.7 |
8.13, 8.14, 8.15 |
| 15 |
Sections 9.1, 9.2 and 9.3 (part) |
9.1, 9.4, 9.6, 9.7, 9.10 |
| 16 |
Sections 9.3 (rest), 9.4 to 9.7 |
9.11, 9.12, 9.14, 9.15, 9.16 |
| 17 |
Sections 11.1 to 11.5 |
11.1, 11.2, 11.3, 11.4 |
| 18 |
Sections 11.6 - 8 & Chap 12 |
11.5, 11.6 |
| 19 |
Chapter 13 |
13.2, 13.4, 13.5, 13.6 |
Hints to exercises
For each of the exercises in the advisory work schedule
hints will be available when you click on the link (any simple
numerical answers will be given). The links will only work for the
exercises up to and including the current week.
Homework problems & solutions
The homework problems will be linked here as .pdf files and you should
print your own copies. I will provide printed copies of the solutions
with the marked homework.
Tables
You will need to use the table of the Standard Normal distribution
during this course, this can be found here.
Exam
This module has a 3 hour exam. You have to answer 4 out of 6 questions from
Section A and 3 out of 4 questions from Section B. Past exams can be
found by following the link from the module page (go back to the index
page and click on the module code -- there is no exam from 2004).
Iain MacPhee
Last modified: 8 March 2007