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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.
June
1, 2011 |
I have
loaded a series of video on www.youku for final examination review.
I have went through the three ways to predict the future: pure random
walk, time series, and regression. For random walk and time series,
I have worked through several questions from Hull. For regression,
I have prepared a question that was worked through including testing
of the regression results. Please visit www.youku.com, log in (or
sign up and sign in), search "UIC MATH 2030" and you should
be able to find the video. There should be 10 video in total, 1
on introduction, 2 on Wiener process, 3 on EWMA, 2 on GARTH (1,1),
and 2 on regression. Please send me email at thomaswu@uic.edu.hk
if there are any questions. |
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May
18, 2011 |
For
our next (and last) class, we will do practise questions. The supplementary
material on options and risk management
strategies and hypothesis testing
and confidence interval. |
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May
14, 2011 |
Our
make up class will be held this coming Wednesday night May 18 from
6pm to 8:50pm in Room C210. |
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May
12, 2011 |
This
is the excel spreadsheet with the build
in Black Scholes option pricing formula and the z-table for
you to play with. You can check the use of the z-table to do from
d1 and d2 to N(d1) and N(d2). |
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May
4, 2011 |
I have
updated the textbook reading part to reflect better what you should
read for this course. Please check outline below and Course Outline
and Lecture Notes session below for more details. In addition, I
want to confirm that the textbook for this course is Hull's Options,
Futures, and Other Derivatives, 7th Edition; this is the more advanced
full edition of his book and hence some of the more difficult part
of the chapters are not covered in this course. I have mistaken
stated before that our class uses the other Hull book but that is
not the case. The other two textbooks from which materials are drawn
are available from the library, but we are only using a small part
of those two textbooks. We will discuss in more details the extent
of textbook material that we will cover for the final exam. We have
several lectures remaining and we will go through the following
topics: |
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- Black
Scholes option pricing model (Hull Chapter 13) - use to value
call and put options,
- Capital
markets efficiency,
- Wiener
processes and Ito's Lemma (Hull Chapter 12) - use to model price
change in the future,
- Estimating
volatilities and correlations (Hull Chapter 19) - using ARMA,
ARCH, GARCH to model price change in the future,
- Regression
(lecture slides) - use regression to predict an unknown variable
(e.g. stock price),
- review
for final examination.
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May
4, 2011 |
Please
check the following dates for dates for make up class and tutorial
sessions that we can held. |
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- May
6 Friday - anytime
- May
7 Saturday - before 3pm
- May
9 Monday - 5pm to 8pm (or partial)
- May
16 Monday - 5pm to 8pm (or partial)
- May
17 Tuesday - before 3pm
- May
18 Wednesday - anytime
- May
19 Thursday - before 3pm
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April
19, 2011 |
I have
located a set of slides on CAPM that is slightly more detailed than
what we have. Slide set 1 and
Slide set 2. You can also check
out books like Investment by Bodie which should be available at
the library for more detailed information. |
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April
18, 2011 |
We
went through the review today for the mid-term test. Here are some
of the questions that we had went through. To download: marked
notes from class, answers for
ch 4 questions #1, answers
for ch 4 questions #2. |
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April
18, 2011 |
As
mentioned in Ms Qin's email, the combined mid-term test will be
held next Wednesday April 20 from 8 pm to 10 pm in room B201. We
will do a short review during next Monday's class; hence please
review the taught material so far and email any questions that you
have to me so that we can go through in class next Monday. |
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April
9, 2011 |
We
are planning to have a common set of mid-term test questions for
all three of the financial mathematics classes. As such, we would
like to have all three classes take the mid-term test at the same
time. We are looking at three possible nights for the mid-term test.
They are on the night of Monday April 18, night of Tuesday April
19, or night of Wednesday April 20. Please send an email to myself
and our TA if you are NOT available for any one of those three nights.
Thanks. In terms of what is covered, we will discuss more during
class on Monday April 11. |
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April
8, 2011 |
As
we will have a mid-term test for our class, I propose we have the
make up class before the mid-term test to make sure that we are
on track for our teaching schedule. These are possible dates and
time for your selection, please review your schedule so that we
can discuss and finalize in our next class on April 11. Week of
April 25 Monday to Friday, May 2, 4, 6, 10, 11, 13, and 18 any time;
May 3, 5, 9, 12, 16, 17, and 19 any time before 3pm. |
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April
5, 2011 |
We
will have a mid-term test which will account for 20% of the final
grade. Details to be announced in the next class. I have posted
the excel answer key to assignment two and the questions to our
quiz on April 4. |
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April
4, 2011 |
Assignment
2 was due today, but unfortunately there was some problems with
the space quota of my email account. As such, many assignments that
were submitted I did not received. To resolve such a situation,
please Forward your original email that was used to submitted your
assignment to allthomasemail@gmail.com. |
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March
30, 2011 |
I have
went over what is required for assignment 2 during class on Monday
March 28 2011, I have also showed how the submitted assignment should
look like within Excel, if you are not clear, please check with
your classmates. For the submission of the assignment, please email
to myself AND our new TA (her email address is listed below) the
actual Excel files, with answers to the assignments questions written
in the body of the email. The time stamp at which I receive your
email is the standard used for the time of receipt. It would solely
be your responsibility to make sure that I receive your assignment
submission on time, which is before class on Monday April 4 2011.
Please make sure that you start on this assignment early; while
I am happy to help with any questions that you might have, it does
not guarantee that I would be able to answer any last minute that
you might have if you start too late (e.g. the night before it is
due). |
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March
23, 2011 |
Due
to foggy weather on Monday March 21 there was no ferry from Hong
Kong to Zhuhai or Macau until late afternoon and as such no class
was held on that day. However a quiz and an homework assignment
(assignment two) was given on that day. The homework assignment
will be due on Monday April 4 (in two week's time) as I will provide
more details of what is required during class on Monday March 28.
Assignment two is available for download in the Assessment Information
section. For the quiz on Monday March 21, it is the initial part
of assignment two and the answer will be provided when we go through
assignment two in the near future. |
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March
2 , 2011 |
Please
bring calculator to class from now on. |
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February
28, 2011 |
Assignment
1 is available in the Assessment section, it is due before class
on March 7, 2011 in hard copy form. |
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February
17, 2011 |
Lecture
slides for Monday February 21 have been posted. It will be used
for both lecture 2 and lecture 3. |
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February
16, 2011 |
Please
work through the questions below on time value of money and annuity.
We will work on these in class next Monday. |
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Cornerstone
Bank pays interest of 3.5 percent compounded annually. Uptown Bank
pays 3.75 percent simple interest. Which one of the following statements
is true if you invest $1,000 in each bank for five years?
a. Cornerstone Bank will pay you a total of $176.59 in interest
over the five years.
b. Uptown Bank will pay you $15.30 less interest over the five years
than Cornerstone Bank will.
c. Cornerstone Bank will pay you a total of $175.00 in interest
over the five years.
d. Uptown Bank will pay you $0.19 less interest than Cornerstone
Bank over the five years. |
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Sun
borrows $13,500 today at 7.90 percent compounded annually. The terms
of the loan require him to repay the principal and interest in one
lump sum three years from today. How much will he have to pay in
three years? |
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Rosa
wants to have $50,000 in her investment account fifteen years from
now. How much does she
have to deposit today to achieve her goal if she can earn 9.5 percent
compounded annually? |
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You
have been offered a business opportunity that will pay you $57,000
in six years if you invest
$25,000 today. What is the expected rate of return on this investment? |
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Carlos
has $2,413 saved today. He wants to buy a different vehicle as soon
as he has $2,700 saved. How long does he have to wait to get his
vehicle if he earns 4.5 percent compounded annually? |
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You
are going to receive $6,000 at the end of each quarter for the next
five years. What is the net
present value of these payments at a discount rate of 7 percent,
compounded quarterly? |
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What
is the future value of the payments in the above question provided
discount rate of 7 percent and compounded quarterly? Can the future
value of the annuity reconciled with the net present value found
above? |
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A preferred
stock pays annual dividends of $1.75. How much are you willing to
pay today to buy one share of this stock if you want to earn a 12.5
percent rate of return? |
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What
is the effective annual rate of 12.5 percent compounded monthly? |
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What
is the effective annual rate of 14.7 percent compounded daily? |
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February
14, 2011 |
I
will post here several questions on annuity, annuity due, and perpetual
cash flow for your practice within the next few days. |
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Outline and Lecture Notes || Lecture Review
|| Course Details || Assessment
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
% |
Assignments |
20
% |
Tests |
20
% |
Final
exmination |
50
% |
|
100
% |
Test.
There will be not more than six very short in-class tests based on recently
taught materials. Together with attendance and class participation,
they will make up 30% of the total result for this course.
DOWNLOAD:
test one answer key || test
two answer key || test three answer
key || test four answer key ||
test five answer key
|| test six 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 ||
assignment three || assignment
three answer key
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.
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Outline and Lecture Notes || Lecture Review
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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
14, 2011 |
We
went through the following topics today: |
|
- introduction
to our course,
- introduction
tofinancial markets,
- time
value calculation using PV, FV, t, and i,
- calculation
of simple and compound interest,
- ordinary
annuity and annuity due,
- perpetual
cash flow calculation, and
- conversion
of APR to EAR for comparison.
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February
21, 2011 |
We
went through the following topics today: |
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- practice
questions on time value of money and annuity questions,
- introduction
to continuous compounding,
- calculation
of continuous compounding present value and future value,
- conversion
between continuous and compounding returns,
- introduction
to yield curves,
and
- theories
behind the shapes of the yield curve.
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February
28, 2011 |
We
went through the following topics today: |
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- quiz
on interest conversion and time value of money,
- credit
risk, credit spread, and its components,
- bond
pricing using compounding and continuous interest rates, and
- calculation
of yield to maturity.
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March
7, 2011 |
We
went through the following topics today: |
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- yield
to maturity, realized yield, current yield, and discount yield,
- introduction
to spot / zero rate,
- calculation
of spot / zero rates,
- introduction
to forward rates,
- CAPM,
and
- risk
and return calculations.
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March
14, 2011 |
We
went through the following topics today: |
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- correlation
with the CAPM framework,
- derivation
of the securities market line,
- derivation
of the capital market line,
- conclusion
of the CAPM model, and
- an
introduction of the forward contracts.
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March
21, 2011 |
No
class due to weather condition. Make up class date and location
TBD. |
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March
28, 2011 |
We
went through the following topics today: |
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- review
of what is required for assignment 2 in terms of output and
submission process,
- review
of forward contracts from last lecture,
- introduction
to futures contracts,
- compare
and contrast forward and futures contracts,
- introduction
to options and their payoff profiles,
- introduction
to the binomial tree method of valuation, and
- the
use of binomial tree on underlying asset to calculate the value
of options.
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April
4, 2011 |
We
went through the following topics today: |
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- review
of our topics taught in this course,
- options
terminology,
- option
profits and loss positions calculations,
- option
intrinsic and time value,
- in-the-money,
at-the-money, out-of-money options, and
- use
of binomial tree model to value American call options.
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April
11, 2011 |
We
went through the following topics today: |
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- using
binomial tree to value an European call option, and
- use
to Black-Scholes to value options.
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April
18, 2011 |
We
went through the following topics today: |
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- using
binomial tree to value an American put option,
- review
of topics for mid-term test,
- futures
and options profit and loss determination,
- CAPM
theoretical, calculation of beta using covariance and variance,
and
- interest
rate topics on bond valuation, forward rate determination, interest
rate conversion between compounding and continuous.
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May
9, 2011 |
We
went through the following topics today: |
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- review
of topics covered before the mid-term test,
- outline
of remaining topics to cover before the final examination,
- market
efficiency hypothesis,
- weak,
semi-strong, and strong form efficiency and their implications,
and
- markov
process, wiener process, generalized wiener process, and ito's
lemma.
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May
16, 2011 |
We
went through the following topics today: |
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- regression
concepts to calculation of alpha and beta,
- hypothesis
testing,
- confidence
interval.
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May
18, 2011 |
We
went through the following topics today: |
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- review
of regression concepts from last class,
- use
and calcuation of standard error,
- hypothesis
testing and confidence interval,
- Type
I and Type II errors,
- weighted
moving average and exponentially weighted moving average model
of volatility estimation,
- ARCH
and GARCH model of volatility estimation,
- review
of option basics,
- review
of option risk management strategies covered call and protective
put,
- binomial
tree valuation of option prices.
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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, marked lecture slides) |
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February
14, 2011 |
Introduction
to financial mathematics, logistics, and other details |
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PART
II. BASIC FINANCIAL CALCULATIONS. |
Lecture
2 |
Reading:
RWJJ Chapter 10 (DOWNLOAD:
lecture slides, marked
lecture slides) |
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February
21, 2011 |
Time
value of money, simple interest, periodic compounding, continuous
compounding, zero rates, forward rate, forward rate agreements,
bond pricing, duration, convexity. |
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Lecture
3 |
Reading:
RWJJ Chapter 10 and Hull Chapter 4 (DOWNLOAD:
marked lecture slides) |
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February
28, 2011 |
Time
value of money, simple interest, periodic compounding, continuous
compounding, zero rates, forward rate, forward rate agreements,
bond pricing, duration, convexity. |
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PART
III. STATISTICAL METHODS IN FINANCE and PORTFOLIO OPTIMIZATION.
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Lecture
4 |
Reading:
Hull Chapter 4 and 1 (DOWNLOAD:
lecture slides) |
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March
7, 2011 |
Return
distribution, variance 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 1 (DOWNLOAD:
lecture slides) |
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March
14, 2011 |
Return
distribution, variance 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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PART
IV. RETURN FORECASTING MODELS |
Lecture
6 |
Reading:
Hull Chapter 11 (DOWNLOAD:
lecture slides) |
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March
28, 2011 |
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 |
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April
4, 2011 |
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
8 |
Reading:
Hull Chapter 12 (DOWNLOAD:
lecture slides) |
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April
11, 2011 |
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
9 |
Reading:
Hull Chapter 13 (13.1-13.4 only) (DOWNLOAD:
lecture slides) |
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April
18, 2011 |
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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April
20, 2011 |
Mid-term
test at B201 8 pm to 10 pm. |
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Lecture
10 |
Reading:
Hull Chapter 12 and 13 (13.1-13.4 only)(DOWNLOAD:
lecture slides) |
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May
9, 2011 |
Black
Scholes option pricing model. Geometric Brownian motion, Wiener
process and Ito's Lemma. |
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PART
V. REGRESSION TECHNIQUES IN FINANCE & CAPM |
Lecture
11 |
Reading:
Hull Chapter 19 (DOWNLOAD:
lecture slides) |
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May
16, 2011 |
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) |
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May
18, 2011 |
Regression
techniques review, beta estimation, CAPM, single-index model. |
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PART
VI. EVENT STUDIES AND CAPITAL MARKET ANOMALIES |
Lecture
13 |
Reading:
RWJ Chapter 12 (12.6) (DOWNLOAD:
lecture slides) |
|
May
23, 2011 |
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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Outline and Lecture Notes || Lecture Review
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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 (2010-2011) |
|
|
Prerequisites |
MATH
1010 Mathematics for Business |
|
STAT
1010 Statistics for Business |
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|
Time
and Location |
Mondays
1pm to 4pm, C207 |
|
|
Instructor |
Dr.
Thomas Wu |
Office |
B111 |
Office
hours |
By
appointment |
Telephone |
86-756-3620181 |
Email |
thomaswu@uic.edu.hk |
Website |
http://www.drthomaswu.com
(all information for this course can be found here) |
|
|
Teaching
Assistant |
Ms.
Min Qin / Ms. Sunny OuYang |
Email |
minqin@uic.edu.hk
/ 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. |
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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 |
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|
Suggested
Textbook |
Options,
Futures and Other Derivatives by Hull, J.C. 7th Edition,
Prentice Hall ('Hull') |
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|
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.
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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. |
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|
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. |
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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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Information
|