|
All
relevant information on UIC Financial Mathematics Course will
be posted on this website.
Click
to go directly to: (1) Updates, (2) Course
Outline and Lecture Notes, (3) Lecture Review,
(4) Course Details, or (4) Assessment
Information.
UPDATES:
Back
to top || Updates || Course
Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
Please
check here for updates during the semester.
May
30, 2009. I have received several questions on the
format and types of questions in the final examination. The exam
will have two parts: Part I short answer questions - you choose
5 questions out of 6, 5 marks each; Part II problems - you also
choose 5 questions out of 6, 15 marks each. Most of the formula
will be provided. You will have three hours to complete the exam,
so please allocate time based on the marks available. In terms
of the types of questions, the scope is pretty even across the
topics so best to go through our review topics from various lectures.
May
30, 2009. The final exam for this class will be
held on Monday, June 1 at 9:30am and I will be invilgilating for
our class. Due to the ferry schedule from Hong Kong, I would need
to come to Zhuhai on Sunday. As such, if you have questions during
your study, please try to email them to me BEFORE Sunday so that
I can get back to you in a timely manner. Otherwise, due to travel
time and sometimes non-access to the internet, I might not be
able to reply to you as soon as I would prefer. Good luck.
May
21, 2009. In one of our previous lectures, we have
done a binomial tree for an option that has a special payoff (like
Problem 11.19). I have prepared another binomial tree question
with a special payoff. The question can be downloaded
here.
May
15, 2009. Revised answer key for Hull Chapter 21
Assignment question 18 is available for downloading
here. The formula in part (b) of the previously provided answer
key was incorrect and I have provided the answer for the whole
question.
May
13, 2009. The answer for our last quiz is available
in both the Assessment
Information section
and in the Course
Outline and Lecture Notes section. Please download and check
your answer and make sure that you know how to do those calculations.
May
10, 2009. The final examination will be held on
Monday, June 1, 2009 at 9:30am. Please confirm time, date and
location with A/R. Before the exam, I will post other practise
questions with answers here for you to try. I will also post my
reply to questions that I have received here so that they can
be shared. Hence please check back here.
May
6, 2009. The slides for May 7 is available for downloading
in the Course
Outline and Lecture Notes section. There are some pratice
questions within the lecture slides that you can try.
May
4, 2009. The following items are available for downloading
in the Course
Outline and Lecture Notes section. (a) A
set of more detailed slides for regression and hypothesis testing,
(b) an Excel spreadsheet on the calculation of the example from
the last lecture on the calculation of the coefficients and standard
errors, (c) a set of 2 practice questions for you to try for Thursday.
I will post more before Thursday so please check back.
May
1, 2009. For the lecture on May 7, please bring
with you all the previous notes, assignments, and quizzes as we
will do a review during class. Before class, I will also upload
a set of practice questions that you should download and print
and try to calculate before coming to class. The class notes from
April 30 is available for downloading in the Course
Outline and Lecture Notes section. The answer key to Quiz
Four can
be downloaded in the Assessment
Information section.
April
21, 2009. My handwritten notes from the April 16
class is available for downloading in the Course
Outline and Lecture Notes section. On April 23, we will continue
with volatility estimation and then start on regression.
April
9, 2009. My handwritten notes from class is available
for downloading in the Course
Outline and Lecture Notes section. The answer key to Assignment
Two and Quiz Three can
be downloaded in the Assessment
Information section.
April
2, 2009. My handwritten notes from class is available
for downloading in the Course
Outline and Lecture Notes section.
April
1, 2009. I have just uploaded the marked slides
for Chapter 1 Introduction under the date March 12, 2009 in the
Course
Outline and Lecture Notes section.
April
1, 2009. I have uploaded Assignement Two and it
can be downloaded in the Assessment
Information section.
It is due Thursday, April 9.
April
1, 2009. I have added my handwritten notes from
the last three classes (March 12, March 19, and March 26) for
downloading in the Course
Outline and Lecture Notes section.
March
31, 2009. The lecture slides for lectures 8, 9,
and 10 are available for download in the Course
Outline and Lecture Notes section. These three lectures will
provide an introduction to the Black-Scholes option pricing model,
its basic assumptions, and required input for valuation of an
option.
March
30, 2009. Someone asked about the meaning of the
last sentence in Hull Ch 11, Section 11.1 on shorting the portfolio
when the price of the option is less than 0.633. I have prepared
something for that if you are not sure what that means, please
download this and read.
March
26, 2009. The answer key to assignment one can be
downloaded in the Assessment
Information section. Please take note of the comment on question
4.25 part (c) in that section. In addition, I have worked through
all the calculation questions for the practice exercise in Chapter
4; if you have tried those questions for practice and want to
know the answer, you can let me know.
March
20, 2009. For Thursday March 26, 2009, we will do
a quick review of options and the first part of the binomial tree,
then we will continue with the binomial tree the rest of the lecture.
In the tutorial session, we will discuss the assignment that was
submitted. For your homework assignment, please submit via email
to myself and Sunny, thanks.
March
17, 2009. The lecture slides for Thursday March
19, 2009 is available for downloading, please see Course
Outline and Lecture Notes section. We will spend a little
time on FRA first, so please bring last week's lecture notes with
you. We will also spend a few minutes on the assignment at the
beginning of class, please bring your copy of the assignment as
well.
March
15, 2009. Update to my March 8 note. I have decided
to change the Assignment One due date from March 19 to March 26
so you can have one more week to prepare for it. Please try to
do the questions as early as possible so that you can have some
time to ask questions if you have any problems with it.
March
8, 2009. The lecture slides for Thursday March 12,
2009 is available for downloading, please see Course
Outline and Lecture Notes section. Assignment
One is also available for downloading in
the
Assessment Information section; it will
also be distributed to you on Thursday March 12. Assignment One
is due Thursday March 19 before class and the solution will be
discussed in the tutorial session on that day.
March
5, 2009. The marked slides from class today can
be downloaded here. You do not need to print
the document, you can just check this set against yours and add
back handwritten notes that you did not copy down during class.
I have added many additional and supplementary information to
the lecture slides that can help you understand concepts from
the Hull textbook. I have written "INFO
ONLY" on the page; they will not be asked
in the examination, they are just there to help you understand
better the concepts in the book. The review notes from last week
with the compound period conversion examples can be downloaded
here. The answer to the quiz today can be downloaded
here or in the Assessment
Information section. Please note that we will not cover duration
and convexity in this course.
March
4, 2009. I have just uploaded the answer key to
the quiz from two weeks ago. It can be downloaded in the
Assessment Information section. Please also
make sure that you have access to the reading RWJJ Chapter 10
so that you will not miss the reading for the first two lectures.
February
27, 2009. The lecture slides for Thursday March
5, 2009 Lecture 4 is available, a 2 powerpoints per page and a
4 powerpoints per page version are available in the
Course Outline and Lecture Notes section.
As before, there
is also a version that can be translated online.
February
24, 2009. For the lecture on Thursday February 26,
2009, we will finish the part on CAPM from last time. We will
also start to discuss Hull's Chapter 4 Interest Rates. However,
I am adding more details and information to the slides and as
such, the slides for Hull's Chapter 4 will be provided to you
later on. But for the class on Thursday February 26, please make
sure that (1) you bring the lecture slides from last time, and
(2) ensure that you have a copy of the Chapter 10 from the 'RWJJ'
book. If time permits, we will go through some of the questions
on the quiz from last time; regardless, the answer key will be
provided to you.
February
14, 2009. The lecture slides for Thursday February
19, 2009 can be downloaded here. There is
also a version that can be translated online.
February
13, 2009. Please note that there is a change in
the grading criteria in order to ensure consistency between the
three classes. Now attendance accounts for 10%, up to three assignments
account for 20%, up to six quizzes account for 20%, and the final
examination accounts for 50%. Please see Assessment
Information
for more information.
February
13, 2009. The lecture slides that was used on February
12, 2009 is available and can be downloaded here.
The supplementary file that shows the finance system can be downloaded
here.
December
20, 2008.
Course material will be available here when the term starts in
February 2009. Please check back.
Back
to top || Updates || Course
Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
ASSESSMENT
Back
to top || Updates || Course
Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
ALL
in-class quizzes, assignments, mid-term test, and final examination
are INDIVIDUAL effort, meaning that you should
work on your own material and any unscholarly actions prohibited
by the university must be avoided.
I
will post ALL relevant course materials, updated
information, correspondences, and relevant student questions in
the UPDATES section on
this page. Students are responsble to check the UPDATES
section frequently on their own to ensure that they are up-to-date.
I will provide the dates and topics of the updates to easier search.
The
final grade is based on the following parts:
| Attendance,
class participation and discussion |
10
% |
| Assignments |
20
% |
| Quizzes |
20
% |
| Final
exmination |
50
% |
| |
100
% |
Quiz.
There will be not more than six very short in-class quizzes based
on recently taught materials. Together with attendance and class
participation, they will make up 20% of the total result for this
course.
DOWNLOAD:
quiz one answer key || quiz
two answer key || quiz three answer key
|| quiz four answer key ||
quiz five answer key 1 || quiz
five answer key 2 || Hull 21.18 answer key
Assignments.
There will be not more than three short assignments that can be
composed of multiple choice, true-and-false, short answers, and
calculation questions. The focus of the assignments is to direct
students to concepts, information, and calculations that they
would be expected to perform in the final examination. There is
generally a week's time to finish the assignment. The assignments
should be based on individual efforts and each student should
work on their own assignment. The assignment is due before class
starts on the due date. The assignments will make up 20% of the
total result for this course.
DOWNLOAD:
assignment one || assignment
one answer key || assignment two || assignment
two answer key
Note
for Assignment One Question 4.25 Part (c). In part
(c), I have used the equation for continuous compounding to value
the FRA for the answer of $1,124.04. However, when you look at
the RK - RF, I have
used the semi-annual compounding version of the rates for this
equation (so 0.06 - 0.0575186). Someone has came and asked about
this question - since this is continuous compounding and equation
is continuous compounding, should we not convert the semi-annual
compounding to continuous compounding for the correct answer.
In a way, yes it is true in that using a continuous compounding
would be most accurate in theory. HOWEVER, in real life, the FRAs
are priced using semi-annual compounding just like most other
fixed income assets; so this is to be more consistent with market
practice. For the purpose of this assignment, you would be considered
correct either way. If you look at Hull's Chapter 4, Section 4.7
Forward Rate Agreements, the first sentence in the paragraph after
the definition of RK, RF, RM and L, the book has assumed that
"these rates are all measured with a compounding frequency
reflecting the length of the period to which they apply"
meaning that these rates are compounded by however it is stated
and not on a continuous compounding basis.
Final
examination. The final examination will be composed of
multiple choice, true-and-false, short answers, and calculation
questions on financial concepts and materials taught in the course
with an emphasis on materials from the second half of the course.
The final examination will make up for 50% of the total result
for this course.
Back
to top || Updates || Course
Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
LECTURE
REVIEW Back
to top || Updates || Course
Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
A
summary of our discussion during the lecture is provided here
for your reivew.
| February
12, 2009 |
In
this lecture, we discussed the following topics:
-
the logistics of this class including grading policy and
other details (please note that the grading criteria is
change),
- the
nature of consumption goods and investment,
- an
overall of the participants in finance and their roles
(see supplementary file),
- returns
calculations like simple and compound interest, and
- general
discussion on the time value of money including present
value and future value calculations.
|
| |
|
| February
19, 2009 |
We
have looked at the following topics today:
-
time value of money calculation including PV, FV, r, annuity,
and perpetuality,
- the
calculation of expected returns on investments,
- the
calculation of variance and standard deviation on an investment,
- the
effect of correlation on the risk of a portfolio, and
- the
calculation of expected return and risk on a portfolio
with 2 assets.
|
| |
|
| February
26, 2009 |
In
today's lecture, we went through the following items:
- evaluate
the risk and return of a portfolio of two assets with
correlation of less than one,
- determine
the effects on the portfolio risk and return when other
assets are added,
- construction
of the efficient frontier,
- the
addition of the risk free asset for the construction of
the Capital Market Line (CML), and
- a
general discussion on the use of beta.
|
| |
|
| March
5, 2009 |
We
discussed the following topics today:
- compound
frequency and continuous compounding,
- theories
that try to explain the shape of the yield curve or term
structured of itnerest rates,
- bond
pricing, and
- we
started on the zero curve.
|
| |
|
| March
12, 2009 |
Today
we went through the following topics:
- the
reason for the use of zero spot curve,
- how
to derive zero spot curve,
- how
to derive forward rates from the zero spot curve,
- an
introduction to forwards, futures, and options, and
- how
to determine the value of futures.
|
| |
|
| March
19, 2009 |
The
following topics was discussed:
- how
to value FRA,
- option
basics,
- the
risk neutral assumption of the binomial tree, and
- the
derivation of the price of an option using a one-step
binomial tree.
|
| |
|
| March
26, 2009 |
We
went through the following topics:
- call
and put options on a more graphical format with cash flow
implications,
- one
step binomial tree,
- two
step binomial tree, and
- the
pricing of call and put options using binomial trees.
|
| |
|
| April
2, 2009 |
Today
we:
- reviewed
the payoff diagram for spot, futures, and option transactions,
- reviewed
the binomial tree approach to pricing options,
- discussed
the construction of payoff diagrams for options,
- reviewed
how to price put options, European, and American options
using binomial trees,
- started
on the Markov Process and its two assumptions, and
- discussed
various level of market efficiency and their characteristics.
|
| |
|
| April
9, 2009 |
We
started on several new topics today including:
- reviewed
the Markov Process and its two assumptions,
- discussed
the Wiener Process and the generalized Wiener Process,
- use
Ito's Lemma to account for the effects of change in t,
- looked
at how the Black-Scholes option pricing works,
- analyzed
the payoff diagrams of options strategies, and
- calculated
yield to maturity, par yield, and current yield for bonds.
|
| |
|
| April
16, 2009 |
We
discussed the following topics:
- volatility,
- historical
volatility, and
- implied
volatility.
|
| |
|
| April
23, 2009 |
We
did an important topics review before continuing on with
volatility from last week. We have discussed:
- the
important topics that we have and will cover in class,
- a
review of what you should get out of these topics from
this class,
- several
ways to forecast volatility including,
- exponentially
weighted moving average,
- ARCH
model,
- GARTH
(1,1), and
- lastly
we started on our regression discussion.
|
| |
|
| April
30, 2009 |
Today
we went through:
- a
review of volatility estimation using ARCH, exponentially
weighted moving average, GARTH(1,1),
- an
example of regression analysis using a simple example
to calculate alpha and beta,
- the
calculation of the standard errors,
- the
evaluation of regression results using hypothesis significance
testing and confidence interval, and
- a
review of CAPM from the regression angle.
|
| |
|
| May
7 , 2009 |
We
focused on a revision of the topics that was covered in
this course, in particular, we discussed:
- payoff
pattern and expectation of various complex option strategies
like bull spread and leveraged options,
- the
implications of the Wiener Process and Ito's lemma result
on how to formulize a random future price,
- the
use and calculation of various volatility forecasting
model like ARCH, EWMA and GARTH (1,1),
- regression
analysis and hypothsis testing, and
-
how to relate the return of an investment to the overall
market using regression under the CAPM framework.
|
Back
to top || Updates || Course
Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
COURSE
OUTLINE AND LECTURE NOTES Back
to top || Updates || Course
Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
This
course outline is tentative and subject to change based on our
progress. Please check the UPDATES section
and table below for latest information.
Hull
= Options, Futures and Other Derivatives by Hull
RWJJ
= Modern Financial Management by Ross, Westerfield, Jaffe, Jordan
RWJ
= Corporate Finance Fundamentals by Ross, Westerfield, Jordan
| PART
I. INTRODUCTION. Introduction to financial basics, time value
of money, and statistical methods in finance. |
| Lecture
1 |
Reading:
RWJJ Chapter 10 (DOWNLOAD:
lecture slides || lecture
slides for translation || lecture slides
supplementary) |
|
|
| February
12, 2009 |
Introduction
to financial mathematics, logistics, and other details |
|
|
| |
|
|
|
| PART
II. STATISTICAL METHODS IN FINANCE and PORTFOLIO OPTIMIZATION.
|
| Lecture
2 |
Reading:
RWJJ Chapter 10 (DOWNLOAD:
lecture slides || lecture
slides for translation || quiz
one answer key) |
|
|
| February
19, 2009 |
Risk
and return, volatility, correlation |
|
|
| |
|
|
|
| Lecture
3 |
Reading:
RWJJ Chapter 10 and Hull Chapter 4 |
|
|
| February
26, 2009 |
Capital
Asset Pricing Model and interest rates |
|
|
| |
|
|
|
| PART
II. FINANCIAL CALCULATIONS. Interest rate related calculations. |
| Lecture
4 |
Reading:
Hull Chapter 4 and 1 (DOWNLOAD:
lecture slides (2 ppt) || lecture
slides (4 ppt) || lecture slides for
translation || quiz
two answer key) |
|
|
| March
5, 2009 |
Interest
rates and derivatives introduction |
|
|
| |
The
review notes from last week with the compound period conversion
examples can be downloaded here. The
marked slides for Chapter 4 from class today can be downloaded
here. |
|
|
| |
|
|
|
| Lecture
5 |
Reading:
Hull Chapter 1 (DOWNLOAD:
lecture slides || lecture
slides for translation || assignment
one) |
|
|
| March
12, 2009 |
Derivatives
introduction |
|
|
| |
Assignment
One distribution |
|
|
| |
(DOWNLOAD:
handwritten notes from class March 12, 2009) |
|
|
| |
The
marked slides for Chapter 1 can be downloaded
here. |
|
|
| |
|
|
|
| PART
IV. BINOMIAL TREES |
| Lecture
6 |
Reading:
Hull Chapter 11 (DOWNLOAD:
lecture slides || lecture
slides for translation) |
|
|
| March
19, 2009 |
Binomial
trees |
|
|
| |
(DOWNLOAD:
handwritten notes from class March 19, 2009) |
|
|
| |
|
|
|
| Lecture
7 |
Reading:
Hull Chapter 11 |
|
|
| March
26, 2009 |
Binomial
trees |
|
|
| |
Assignment
One due before class
(DOWNLOAD: assignment
one answer key and see Notes in Assessment
Information) |
|
|
|
An
explanation on last sentence on Hull Ch 11, Section 11.1
on shorting the portfolio when price of option is less than
0.633 can be downloaded here. |
|
|
| |
(DOWNLOAD:
handwritten notes from class March 26, 2009) |
|
|
| |
|
|
|
| PART
V. RETURN FORECASTING MODELS |
| Lecture
8 |
Reading:
Hull Chapter 12 (DOWNLOAD:
lecture slides || lecture
slides for translation) |
|
|
| April
2, 2009 |
Wiener
processes and Ito's Lemma |
|
|
| |
Assignment
Two distribution (DOWNLOAD:
assignment
two) |
|
|
| |
(DOWNLOAD:
handwritten notes from class April 2, 2009) |
|
|
| |
|
|
|
| Lecture
9 |
Reading:
Hull Chapter 13 (13.1-13.4 only) (DOWNLOAD:
lecture slides || lecture
slides for translation) |
|
|
| April
9, 2009 |
Black-Scholes-Merton
model |
|
|
| |
Assignment
Two due before class (DOWNLOAD:
assignment two answer key) |
|
|
| |
(DOWNLOAD:
handwritten notes from class April 9, 2009 || quiz
three answer key) |
|
|
| |
|
|
|
| Lecture
10 |
Reading:
Hull Chapter 21 (DOWNLOAD:
lecture slides || lecture
slides for translation) |
|
|
| April
16, 2009 |
Volatilities
and correlations for option pricing |
|
|
| |
(DOWNLOAD:
handwritten notes from class April 16, 2009) |
|
|
| |
| PART
VI. REGRESSION |
| Lecture
11 |
Reading:
Handout to be distributed (DOWNLOAD:
lecture slides || lecture
slides for translation) |
|
|
| April
23, 2009 |
Financial
regression review |
|
|
| |
(DOWNLOAD:
handwritten notes from class April 23, 2009) |
|
|
| |
|
|
|
| Lecture
12 |
Reading:
RWJJ Chapter 10 (10.9) (DOWNLOAD:
lecture slides || lecture
slides for translation ||
quiz four answer key) |
|
|
| April
30, 2009 |
Regression
techniques |
|
|
| |
|
|
|
| PART
VII. CAPITAL MARKETS |
| Lecture
13 |
Reading:
RWJ Chapter 12 (12.6) (DOWNLOAD:
lecture slides || lecture
slides for translation) |
|
|
| May
7, 2009 |
Event
studies and capital market anomalies |
|
|
| |
(DOWNLOAD:
regression review || Excel
example on regression ||
practice questions) |
|
|
| |
(DOWNLOAD:
quiz five answer key
1 || quiz five answer key 2 || Hull
21.18 answer key) |
|
|
Back
to top || Updates || Course
Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
|