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UIC Financial Mathematics

 

 

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.

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.

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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 %
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.

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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 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.

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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 || 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)    

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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 (2008-2009)
  Course outline can be downloaded here.
   
Prerequisites MATH 1010 Mathematics for Business
  STAT 1010 Statistics for Business
   
Time and Location Thursdays 3pm to 6pm. Room B303.
   
Instructor

Dr. Thomas Wu

Office B429 
Office hours Thursdays 1 pm to 2:30 pm (by appointment)
Email thomaswu@uic.edu.hk
Website http://www.drthomaswu.com (all information for this course can be found here)
   
Tutor Sunny Ou Yang
Office F-308
Email ouyangsunny@uic.edu.hk
Telephone  
   
Course Objectives

Fundamental methods for formulating and solving financial models will be developed. Emphasis will be on defining the mathematical structure of problems and on practical computer methods for obtaining model solutions.

   
Suggested Textbook Options, Futures and Other Derivatives by Hull, J.C. 7th Edition, Prentice Hall ('Hull')
   
Suggested Reference

Corporate Finance Fundamentals by Ross, Westerfield, Jordan, 8th Edition, McGraw-Hill ('RWJ') - Chapter 12

  Modern Financial Management by Ross, Westerfield, Jaffe, Jordan, 9th Edition, McGraw-Hill ('RWJJ') - Chapter 10
  These two books are available from the library.
   
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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This website is my personal journal, book case, and notepad. ALL past, present, and future information posted on this website is for my personal use, is of my sole personal opinion, and is not meant to be taken as advice or facts of any kind whatsoever. I hereby denounce ALL responsibilities for any information, recommendation, or action derived from this website. All materials contained in this website is maintained by myself. ANY external use, copying or duplication of materials from this web site are strictly prohibited unless authorized AND properly referenced.