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UIC
Financial Mathematics (MATH 2030)
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
29,
2013 |
Answer
key for the mid-term test and practice
questions from class on Monday. |
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| May
27,
2013 |
The
final examination will be held this Saturday, June 1 from 6 pm
to 9 pm. |
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Please
take note that for the time value of money question that we did
in class (on the retirement), the EAR interest rate given should
be converted to APR monthly term first before being used for the
time value calculation. |
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I will
post some of the practice questions that we have done in class here
after I have organized them. |
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| May
22,
2013 |
Here
are some sources that I think are good for review of hypothesis
testing. Take note that these are based on testing a observed
y, hence the standard deviation is used. In our case, if we are
testing the a / alpha or the b / beta in our regression, then
we should use the standard error instead in the bottom when we
standardize for the test. Please only go through these if you
have forgotten what hypothesis testing is about, if you have adequate
understanding of hypothesis testing, you do not need to go through
these references. To reiterate, the information below are references
only for you to have a better understanding of hypothesis testing,
these are not part of our curriculum and will not included in
our examination. |
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| May
21,
2013 |
The
mid-term test was distributed yesterday during class for you to
review. If there are any question / sections that you would like
clarifications on, please email me and I will go over those parts
in class next Monday. For next Monday, we will continue with volatility
forecasting models and we will do a practice question on regression
analysis and hypothesis testing, then a review session for the final
examination will be held. For our class, the final examination will
be held in the evening of Saturady June 1. |
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| May
19,
2013 |
Lecture
slides on Wiener Process and volatility
estimation. |
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| May
12,
2013 |
Notes
on the no arbitrage argument and risk neutral approach to value
an option. |
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| May
11,
2013 |
Lecture
slides on regression and hypothesis
testing for coming Monday. Notes on no arbitrage and risk neutral
approach will be uploaded later. |
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|
| May
6,
2013 |
example
of using binomial tree to value European and American calls
and puts, the notes for the use of no arbitrage and risk neutral
approach will be uploaded later. |
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| May
2,
2013 |
In
order to be able to do a few more practice questions for pricing
of the American options using the binomial tree, Assignment 5 due
date is now Monday May 13 before class instead of Monday May 6 before
class as discussed in class this Monday. |
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| April
29,
2013 |
Lecture
latest lecture slides on binomial
tree with answers included, the binomial
excel to play with, and assignment
five. |
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| April
22,
2013 |
Lecture
slides for binomial tree marked
and binomial tree unmarked. |
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| April
22,
2013 |
Answer
key to assignment four. |
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| April
19,
2013 |
The
formula sheet that will be
provided to you with the mid-term test, for your reference. |
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| April
13,
2013 |
Answer
key to assignment two and assignment
three. |
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| April
11,
2013 |
Answers
to the practice question on the second interest rate calculation
question, which is the same as the last question in assignment 3.
Full answer set for assignment 2 and assignment 3 will be uploaded
shortly. |
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| April
8,
2013 |
Assigment
Four can be downloaded here.
It
is due in two weeks on Monday April 22, 2013 at the beginning of
class in hard copy form. The answers can be longer and some drawings
might be used so please use new pieces of paper to complete assignment
four. |
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|
| March
30, 2013 |
Answers
to the practice question on the first interest rate calculation
question. |
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| March
26, 2013 |
Answers
to the practice questions on time value of money, futures, and
options that we did in class on March 25. The answer to the two
questions on interest rate calculations will be posted later on. |
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| March
25, 2013 |
As
announced by Sunny today in class, our mid-term test will be held
on Monday April 22, 2013 from 7pm to 9pm. The mid-term test will
cover topics up to and including the CAPM. |
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|
| March
25, 2013 |
I will
upload the practice questions and answers that we did in class in
the next few days. |
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| March
25, 2013 |
Assigment
Three can be downloaded here.
It is due in two weeks on Monday April 8, 2013 at the beginning
of class in hard copy form. Please print the two pages on one piece
of paper using both front and back, and write your name (the one
used for school registration) and student number on top of page
one. |
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| March
19, 2013 |
Answer
for Assignment 1 last week. |
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| March
18, 2013 |
Assigment
Two can be downloaded here.
It is due in one week on Monday March 25, 2013 at the beginning
of class in hard copy form. Please print the two pages on one piece
of paper using both front and back, and write your name (the one
used for school registration) and student number on top of page
one. |
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| March
17, 2013 |
Answer
for the quiz questions last week. |
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| March
10, 2013 |
The
slides for lecture 3 and lecture 4 (and reading) has just been posted. |
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| March
6, 2013 |
Question
received: "Good evening, do you remember Lucy, your pig, you
said we had a forward contract that we would exchange Lucy(S0=$5000)
in the next year, and the price would be $5600. But now you cannot
give me Lucy, so I have to buy another pig in the market. And the
price is higher than our contract price, is $8000. So I will call
you and ask you give me $3000(This story is you tell us in the class).
OK, my question is why is $3000, not $2400. Because if we finished
exchange, I need to pay you is $5600, so I just can ask you for
$2400. Right? When we meet this kind of problem, we need to base
on the S0 or F0 to ask money?" |
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Thanks
for picking up this question. I have made the assumption that the
forward agreement price to buy and sell is at 5000, not the 5600
from the example earlier. So to summarize, you are correct. When
we do cash settlement, we decide how much cash difference to pay
to / receive from the other party by using the price that is set
by the forward agreement, i.e. the futures price. Using the same
example but setting the future price (price in the forward agreement)
at 5600; then if the market price is 8000 then the cash settlement
amount should be 2400 farmer pays restaurant, and if the market
price is 3000 then the cash settlement amount should be 2600 restaurant
pays farmer. |
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| March
4, 2013 |
Assigment
One can be downloaded here.
It is due in one week on Monday March 11, 2013 at the beginning
of class in hard copy form. Please print the two pages on one piece
of paper using both front and back, and write your name (the one
used for school registration) and student number on top of page
one. |
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| March
2, 2013 |
The
slides for lecture 2 has just been posted. |
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| February
25, 2013 |
The
reading from RJWW can be read later for Lecture 3, 4, and 5. Download
here. |
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For
the 8th Edition of Hull, the content is very similar to the 7th
Edition. You can check the Table of Content for both books at the
publisher's website to compare for yourself. |
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Outline and Lecture Notes || Lecture Review
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Information
ASSESSMENT
Back
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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
% |
| Assessments |
20
% |
| Tests |
20
% |
| Final
exmination |
50
% |
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100
% |
Assessments.
There are continuous assessments in the form of assignments and / or
in-class quizzes to ensure that concepts and calculation process are
understood. Together with attendance, in-class participation, and discussion,
they will make up 30% of the total result for this course.
[assignment
one , assignment two, assignment
three, assignment
four, assignment
five]
Tests.
There will be a mid-term test on the week of April 22, 2013. Topics
covered before that date will be covered in this mid-term test. This
mid-term test will make up 20% of the total result for this course.
Final
examination. The final examination can be composed of multiple
choice, true-and-false, short answers, and calculation questions on
financial concepts, materials, and calculations 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.
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Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
LECTURE
REVIEW Back
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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
25, 2013 |
We
went through the following topics today: |
|
- introduction
to financial mathematics,
- preview
of topics to be covered for the course,
- time
value of money,
- calcuation
of present value, future value, interest rate, and time for
single cash flow,
- calculation
of ordinary annuity and annuity due for a series of cash flow,
and
- present
value of a perpetual cash flow.
|
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|
March
4,
2013 |
We
went through the following topics today: |
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- assignment
of assignment one,
- review
of time value of money,
- calculation
of APR and EAR,
- introduction
to financial derivatives,
- introduction
to forwards and futures,
- determination
of forward / futures prices,
- payoff
of forward / futures,
- comparison
between forward and futures, and
- advantages
and disadvantages of forward and futures.
|
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March
11,
2013 |
We
went through the following topics today: |
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- review
of answers to assignment one,
- short
quiz on APR / EAR and annuities,
- introduction
to options,
- introduction
to returns calculations, and
- periodic
and continuous compounding.
|
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March
18,
2013 |
We
went through the following topics today: |
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- assignment
of assignment two,
- review
of periodic and continuous compounding,
- bond
valuation using both periodic and continuous compounding,
- returns
calculations for fixed income investments,
- zero
rates calcuation, and
- introduction
to Capital Asset Pricing Model (CAPM).
|
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March
25,
2013 |
We
went through the following topics today: |
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- assignment
of assignment three,
- practice
questions on time value of money and derivatives,
- practice
questions on interest rate calculations,
- introduction
to Capital Asset Pricing Model (CAPM),
- introduction
to calculation of return and risk for one asset, and
- introduction
to calculation of return and risk for more than one asset.
|
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April
8,
2013 |
We
went through the following topics today: |
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- went
through answers to assignment two,
- went
through answers to assignment three,
- assignment
of assignment four,
- calculation
of risk and return for one asset,
- calculation
of risk and return for more than one asset,
- calculation
of covariance and correlation,
- calculation
of portfolio risk and return, and
- the
benefits of diversification.
|
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|
April
15,
2013 |
We
went through the following topics today: |
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- review
of calculation of risk and return for one asset,
- review
of calcuation of risk, return, covariance, and correlation
of two assets,
- extension
from investment in two assets to multiple assets in terms
of risk and return,
- efficient
frontier, minimum variance portfolio, and dominated portfolio,
- introduction
of risk free asset to the efficient frontier,
- construction
of the capital markets line (CML),
- systematic
versus non-systematic risk and benefits of diversification,
- separation
theory on the investment and financing decisions,
- introduction
to beta,
- calculation
of beta with covariance between asset and market portoflio,
and
- use
of CAPM formula.
- [download:
our CAPM step-by-step note
from the class]
|
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April
22,
2013 |
We
went through the following topics today: |
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|
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April
29,
2013 |
We
went through the following topics today: |
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use
of binomial tree to value european and american calls and puts.
[download:
lecture slides on binomial tree
with answers included, the binomial
excel to play with, and assignment
five. |
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|
May
6,
2013 |
We
went through the following topics today: |
| |
- example
of using binomial tree to value european and american
calls and puts, and
- using
no arbitrage and risk neutral approach to price an option
with a one step tree (will upload later).
|
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|
May
13,
2013 |
We
went through the following topics today: |
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- review
of assignment five answers,
- introduction
to regression analysis,
- calculation
of the coefficients a and b in a regression equation, and
- calculation
of standard errors for a and b.
- [download:
assignment 5 answer,
quiz answer]
|
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May
20,
2013 |
We
went through the following topics today: |
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- review
of regression from last week,
- hypothesis
testing, and
- Wiener
process.
|
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|
May
27,
2013 |
We
went through the following topics today: |
| |
- review
of the Wiener Process,
- volatility
forecasting using the ARCH, EWMA, and GARCH approaches,
- review
of final examination topics, and
- worked
on practice questions on time value of money, regression,
and hypothesis testing.
|
Back
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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:
Time value of money (DOWNLOAD:
lecture slides, marked
lecture slides) |
|
| February
25, 2013 |
Introduction
to financial mathematics, logistics, time value of money, and other
details |
|
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|
|
| PART
II. BASIC FINANCIAL CALCULATIONS. |
| Lecture
2 |
Reading:
Hull Chapter 1 (DOWNLOAD:
lecture slides, assignment
one) |
|
| March
4, 2013 |
Futures
/ forward rate, forward rate agreements, futures contracts, and
options. |
|
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|
|
| Lecture
3 |
Reading:
Hull Chapter 4 (DOWNLOAD:
lecture slides) |
|
| March
11, 2013 |
Simple
interest, periodic compounding, continuous compounding, and zero
rates. |
|
| |
|
|
| PART
III. STATISTICAL METHODS IN FINANCE and PORTFOLIO OPTIMIZATION.
|
| Lecture
4 |
Reading:
RWJJ Chapter 10 (DOWNLOAD:
lecture slides, ch
10 reading,
assignment two) |
|
| March
18, 2013 |
Capital
Asset Pricing Model (CAPM), return distribution, variance and standard
deviation as a volatility measure, return correlations and co-variances,
portfolio mean and variance, two-asset portfolio optimization, multiple-asset
portfolio optimization, efficient portfolio. |
|
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|
| Lecture
5 |
Reading:
Hull Chapter 11 (DOWNLOAD:
lecture slides, assignment
three) |
|
| March
25, 2013 |
Binomial
trees. |
|
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|
|
| PART
IV. RETURN FORECASTING MODELS |
| Lecture
6 |
Reading:
Hull Chapter 11 (DOWNLOAD:
assignment
four) |
|
| April
8, 2013 |
Discrete
model of stock price movement: Binomial Trees. One-step binomial
tree, no-arbitrage argument, risk-neutral valuation, multiple-step
binomial tree, American options, Delta.
Geometric Brownian motion, log-normal return, GARCH models, ARMA
models.
|
|
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|
|
| Lecture
7 |
Reading:
Hull Chapter 11 |
|
| April
15, 2013 |
Discrete
model of stock price movement: Binomial Trees. One-step binomial
tree, no-arbitrage argument, risk-neutral valuation, multiple-step
binomial tree, American options, Delta.
Geometric Brownian motion, log-normal return, GARCH models, ARMA
models. |
|
| |
|
|
| Lecture
8 |
Reading:
Hull Chapter 12 |
|
| April
22, 2013 |
Discrete
model of stock price movement: Binomial Trees. One-step binomial
tree, no-arbitrage argument, risk-neutral valuation, multiple-step
binomial tree, American options, Delta.
Geometric Brownian motion, log-normal return, GARCH models, ARMA
models. |
|
| |
|
|
| April
22, 2013 |
Mid-term
test from 7 to 9 pm, room B202 |
|
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|
|
| Lecture
9 |
Reading:
Hull Chapter 13 (13.1-13.4 only) (DOWNLOAD:
lecture slides, assignment
five) |
|
| April
29, 2013 |
Discrete
model of stock price movement: Binomial Trees. One-step binomial
tree, no-arbitrage argument, risk-neutral valuation, multiple-step
binomial tree, American options, Delta.
Geometric Brownian motion, log-normal return, GARCH models, ARMA
models. |
|
| |
|
|
| Lecture
10 |
Reading:
Hull Chapter 12 and 13 (13.1-13.4 only) |
|
| May
6, 2013 |
Black
Scholes option pricing model. Geometric Brownian motion, Wiener
process and Ito's Lemma. |
|
| |
| PART
V. REGRESSION TECHNIQUES IN FINANCE & CAPM |
| Lecture
11 |
Reading:
Hull Chapter 19 (DOWNLOAD:
lecture slides on regression,
lecture slides on hypothese testing) |
|
| May
13, 2013 |
Estimating
volatility and correlation using ARMA, ARCH, and GARCH models. |
|
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|
|
| Lecture
12 |
Reading:
RWJJ Chapter 10 (10.9) (DOWNLOAD:
lecture slides on Wiener and volatility
estimation) |
|
| May
20, 2013 |
Regression
techniques review, beta estimation, CAPM, single-index model. |
|
| |
|
|
| PART
VI. EVENT STUDIES AND CAPITAL MARKET ANOMALIES |
| Lecture
13 |
Reading:
RWJ Chapter 12 (12.6) |
|
| May
27, 2013 |
Three
forms of efficient capital market and requirements for an efficient
capital market, types of anomalies that arise in capital market. |
|
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|
|
| June
1, 2013 |
Final
examination 6pm to 9pm. |
|
Back
to top || Updates || Course
Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
COURSE
DETAILS Back
to top || Updates || Course
Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
Information
| Course |
MATH
2030, Financial Mathematics, Semester II (2012-2013) |
| |
|
| Prerequisites |
MATH
1010 Mathematics for Business |
| |
STAT
1010 Statistics for Business |
| |
|
| Time
and Location |
By
appointment |
| |
|
| Instructor |
Dr.
Thomas Wu |
| Office |
C129 |
| Office
hours |
By
appointment |
| Email |
thomaswu@uic.edu.hk |
| Website |
http://www.drthomaswu.com
(all information for this course can be found here) |
| |
|
| Teaching
Assistant |
Ms.
Sunny OuYang |
| Email |
ouyangsunny@uic.edu.hk |
| |
|
| Course
Objectives |
Fundamental
methods for formulating and solving financial models will be developed.
Emphasis will be on defining the mathematical structure of problems. |
| |
|
| Learning
Outcomes |
(a)
Knowledge - Basic Financial calculations, Statistical
Methods in Finance & Portfolio Optimization, Return Forecasting
Models, Regression techniques in Finance & CAPM, Event Studies
and Capital Market Anomalies
(b) Skills - Basic financial modeling skills
and quantitative methods to solve the financial problems.
(c) Attitude |
| |
|
| Suggested
Textbook |
Options,
Futures and Other Derivatives by Hull, J.C. 7th Edition,
Prentice Hall ('Hull') |
| |
|
| Suggested
Reference |
Fundamentals
of Corporate Finance by Ross, Westerfield, Jordan,
8th Edition, McGraw-Hill ('RWJ') |
| |
Modern
Financial Management by Ross, Westerfield, Jaffe,
Jordan, 9th Edition, McGraw-Hill ('RWJJ')
|
| |
Mathematics
for Finance: An Introduction to Financial Engineering,
by Capinski and Zastawniak, 2003, Springer |
| |
Stochastic
Calculus for Finance I, Shreve, 2004, Springer |
| |
Stochastic
Calculus for Finance II, Shreve, 2004, Springer |
| |
|
| Teaching
Method |
There
are two lecture hours and a one tutorial hour per week. Students
are required to attend all lectures and tutorials. Students are
expected to read the assigned reading materials (or chapters)
prior to the lecture and complete their assignments before the
tutorials.
In
the tutorials, discussions will be based on the topics related
to the materials in the preceding lectures and will be in the
form of problem discussions.
|
| |
|
| Grading
Policy |
All
university policies concerning acceptable student behavior apply
for this course. In particular, unscholarly actions prohibited by
the university should be avoided to prevent regretable results from
these actions. |
| |
|
| Calculator
Policy |
For
this course, a general purpose non-financial calcuator can be
used. Students who do not have ready access
to a financial calculator should be able to perform all the required
analysis and calculations using a general purpose non-financial
calculator for the tutorials, assignments, mid-term test, and
final examination.
You
can also use a non-programmable financial calculator for the tutorials,
assignment, mid-term test, and final examination. Common financial
calculators are HP12c and TI BAII PLUS. User manual in simplified
chinese and a tutorial for the HP12c can
be found here and a simple tutorial for the HP12c can
be found here. User manual for the TI BAII can
be found here.
Regardless
of the types of calculators used for this course, students are
responsible for their own equipment and they cannot be shared
in a quiz, test, or examination situation. As a result, students
MUST bring their own calculators to each class. In addition, each
student must be proficient in the use of their own equipment.
Electronic
translators CANNOT be used for quiz, test, or examination situations,
but they can be used during class (only with volume off) and your
own study time. |
| |
|
| Financial
Terms |
There
are specific terms that apply to accounting and finance, and there
are various online sources that can help students understand these
terms.
Download
and print for reference:
Online
finance dictionaries:
Other
unverified sources of financial references:
|
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Outline and Lecture Notes || Lecture Review
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Information
|