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UIC Financial Mathematics (MATH 2030)

 

 

All relevant information on UIC Financial Mathematics Course will be posted on this website.

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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.
   
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.
   
May 14, 2011 Our make up class will be held this coming Wednesday night May 18 from 6pm to 8:50pm in Room C210.
   
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).
   
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:
 
  • 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.
   
May 4, 2011 Please check the following dates for dates for make up class and tutorial sessions that we can held.
 
  • 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
   
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.
   
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.
   
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.
   
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.
   
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.
   
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.
   
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.
   
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).
   
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.
   
March 2 , 2011 Please bring calculator to class from now on.
   
February 28, 2011 Assignment 1 is available in the Assessment section, it is due before class on March 7, 2011 in hard copy form.
   
February 17, 2011 Lecture slides for Monday February 21 have been posted. It will be used for both lecture 2 and lecture 3.
   
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.
   
  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.
   
  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?
   
  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?
   
  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?
   
  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?
   
  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?
   
  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?
   
  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?
   
  What is the effective annual rate of 12.5 percent compounded monthly?
   
  What is the effective annual rate of 14.7 percent compounded daily?
   
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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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 %
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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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 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.
   
February 21, 2011 We went through the following topics today:
 
  • 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.
   
February 28, 2011 We went through the following topics today:
 
  • 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.
   
March 7, 2011 We went through the following topics today:
 
  • 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.
   
March 14, 2011 We went through the following topics today:
 
  • 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.
   
March 21, 2011 No class due to weather condition. Make up class date and location TBD.
   
March 28, 2011 We went through the following topics today:
 
  • 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.
   
April 4, 2011 We went through the following topics today:
 
  • 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.
   
April 11, 2011 We went through the following topics today:
 
  • using binomial tree to value an European call option, and
  • use to Black-Scholes to value options.
   
April 18, 2011 We went through the following topics today:
 
  • 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.
   
May 9, 2011 We went through the following topics today:
 
  • 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.
   
May 16, 2011 We went through the following topics today:
 
  • regression concepts to calculation of alpha and beta,
  • hypothesis testing,
  • confidence interval.
   
May 18, 2011 We went through the following topics today:
  • 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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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)  
February 14, 2011
Introduction to financial mathematics, logistics, and other details  
 
   
PART II. BASIC FINANCIAL CALCULATIONS.
Lecture 2
Reading: RWJJ Chapter 10 (DOWNLOAD: lecture slides, marked lecture slides)   
February 21, 2011
Time value of money, simple interest, periodic compounding, continuous compounding, zero rates, forward rate, forward rate agreements, bond pricing, duration, convexity.   
 
    
Lecture 3
Reading: RWJJ Chapter 10 and Hull Chapter 4 (DOWNLOAD: marked lecture slides)   
February 28, 2011
Time value of money, simple interest, periodic compounding, continuous compounding, zero rates, forward rate, forward rate agreements, bond pricing, duration, convexity.   
 
    
PART III. STATISTICAL METHODS IN FINANCE and PORTFOLIO OPTIMIZATION.
Lecture 4
Reading: Hull Chapter 4 and 1 (DOWNLOAD: lecture slides)   
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.   
 
    
Lecture 5
Reading: Hull Chapter 1 (DOWNLOAD: lecture slides)   
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.   
 
    
PART IV. RETURN FORECASTING MODELS
Lecture 6
Reading: Hull Chapter 11 (DOWNLOAD: lecture slides)   
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.
  
 
    
Lecture 7
Reading: Hull Chapter 11   
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.
  
 
    
Lecture 8
Reading: Hull Chapter 12 (DOWNLOAD: lecture slides)   
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.
  
   
Lecture 9
Reading: Hull Chapter 13 (13.1-13.4 only) (DOWNLOAD: lecture slides)   
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.
  
     
April 20, 2011 Mid-term test at B201 8 pm to 10 pm.  
 
    
Lecture 10
Reading: Hull Chapter 12 and 13 (13.1-13.4 only)(DOWNLOAD: lecture slides)   
May 9, 2011
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)   
May 16, 2011
Estimating volatility and correlation using ARMA, ARCH, and GARCH models.   
   
Lecture 12
Reading: RWJJ Chapter 10 (10.9) (DOWNLOAD: lecture slides)   
May 18, 2011
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) (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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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
   
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.

 
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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