sample course outline ckmt 802 financial mathematics ii

SAMPLE COURSE OUTLINE
CKMT 802
FINANCIAL MATHEMATICS II
This is a sample course outline only. It should not be used to plan assignments or purchase textbooks.
A current version of the course outline will be provided by the instructor once the course begins.
Every effort will be made to manage the course as stated. However, adjustments may be necessary at the
discretion of the instructor. If so, students will be advised and alterations discussed in the class prior to
implementation.
It is the responsibility of students to ensure that they understand the University’s policies and procedures,
in particular those relating to course management and academic integrity
COURSE DESCRIPTION
This course covers fixed income derivatives and the quantitative aspects of risk and portfolio management
in modern finance. It first introduces single factor interest rate models and pricing of fixed income
derivatives. An analysis of risk measures and their properties will be provided with special emphasis on
market and credit risk. An overview of other types of risks will be quickly mentioned. The course also
develops portfolio optimization techniques. Case studies and a partial preparation for financial
certification programs (FRM and PRM) will be provided.
This course is designed to provide students with an understanding of Risk Assessment and Management.
Three broad areas will be examined:
Interest rate models and fixed income pricing.
Analysis of Risk measures.
Risk Management of Portfolios.
COURSE OBJECTIVE/LEARNING OUTCOMES
To provide students with basics tools to model and price fixed income securities.
To provide an overview of risk measures, the context where they apply as well as practical
examples of their use.
To provide a sound foundation of risk management as preparation for FRM/PRM certificates.
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Financial Mathematics I I CKMT 802

CORE TOPICS:
Interest rate Modeling and Pricing: Fixed income markets are the largest capital markets in the world.
They involve a large and diverse set of participants including governments, banks, private and
institutional investors. This part of the course has two objectives, first is to provide students with the
theoretical framework to deal with the analysis of fixed income securities and derivatives. Second to use
this theory in the case of a simple model, the Vasicek model.
Risk Measures: Risk measures are defined mainly in the context of Maket and Credit scenarios. They are
used to determine the amount of an asset to be kept in reserve in order to make the risks taken by financial
institutions, such as banks and insurance companies, acceptable to the regulator. Particular emphasis will
be placed on standard measures like variance and Value-at-Risk as well as convex and coherent risk
measurement like Expected Shortfall.
Portfolio Risk Management: The concept of risk and return, in particular expected value and volatility of
a portfolio will be provided. Optimization problems associate with portfolio management like finding
efficient portfolios, efficient frontier, with and without risky assets will be studied in detail.
Financial Data: Hands on applications will be presented using toy financial data in order to establish a
foundation for the use of Matlab in Financial Mathematics.
TEXTBOOK AND READING LISTS
This is a sample course outline only. It should not be used to purchase textbooks. A current version
of the course outline will be provided by the instructor once the course begins.
Required Text:
(1) Financial Risk Manager Handbook, Jorion, Ph. John Wiley & Sons, Inc. Second Edition
(2) Investment Science. Luenberger D.G. Oxford University Press. 2nd edition(1998)
Readings and Related Material:
Bond Markets, Analysis, And Strategies, Pearson. Prentice Hall, 6th edition, Frank J. Fabozzi.(2007)
COURSE STRUCTURE AND ORGANIZATION
This is a sample course outline only. A current version of the course outline will be provided by the
instructor once the course begins.
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Financial Mathematics I I CKMT 802

Each class will consist of two components: A lecture that covers theory and an overview of practical
applications of concepts and a demonstration of the concepts in financial applications.
Week Topic Details
1 Interest rate Models.
Chapter 7 (1): Overview of Single Factor models.
2 Pricing fixed Income.
3 Market Risk models
Pricing fixed income securities with Vasicek Model. Non
defaultable vanilla bonds pricing.
Chapter 11 (1): Methods for Value-at-Risk calculation. Delta-
Gamma approach for portfolio VaR.
4
Coherent risk measures.
Assignment 1
Expected Shortfall. Stress scenario and back testing
techniques.
Interest rate Pricing.
5 Credit Models.
Part 4 (1): Structural models and Reduced-form models.
6
Credit Risk Management.
Assignment 1 Due
Default probabilities and recovery models.
-
7 Credit Rating Credit portfolio losses and credit VaR. Rating methods.
8
Other types of risk
Assignment 2
Chapter 24 (1): Operational Risk. Liquidity Risk.
Risk Measures.
9 Portfolio Management
Chapter 6 (2): Expected Return and Volatility of a portfolio.
10 Case Study 2
Mean-Variance Portfolio optimization (MVPO): risky assets.
11 Mapping Population MVPO: risky and risk-free assets. Value at Risk Portfolio
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Financial Mathematics I I CKMT 802

Projections
Assignment 3
Assignment 2 Due
Optimization.
Portfolio Optimization.
-
12 Capital Asset Pricing
Model.
Chapter 7 (2): Capital Asset Pricing Model.
13 Exam Exam: Multiple Choice/Short Answer
METHOD AND SCHEDULE OF STUDENT EVALUATION
This is a sample course outline only. It should not be used to plan assignments. A current version of the
course outline will be provided by the instructor once the course begins.
3 assignments worth 20% each 60%
Final examination (non-lab) 40%
Total 100%
Lab Assignments (graded):
Assignment 1: Pricing of fixed income derivatives under Vasicek model.
Assignment 2: Calculation of Risk Measures in several scenarios.
Assignment 3: Mean Variance Portfolio allocation with risky and non-risky assets.
Assignments are due at the beginning of the evening set out in the schedule above. The instructor must
approve any extension prior to the due date. No lab assignment submission will be accepted for
grading once graded labs have been returned to students, normally at the next class after being
handed in. Work not handed in during class may be e-mailed to …@ryerson.ca.
MISSED TERM WORK OR EXAMINATIONS
Students are expected to complete all assignments, tests, and exams within the time frames and by the
dates indicated in this outline. Exemption or deferral of an assignment, term test, or final examination is
only permitted for a medical or personal emergency or due to religious observance. The instructor must
be notified by e-mail prior to the due date or test/exam date, and the appropriate documentation must be
submitted. For absence on medical grounds, an official student medical certificate, downloaded from the
Ryerson website at http://www.ryerson.ca/senate/forms/medical.pdf or picked up from The Chang
School at Heaslip House, 297 Victoria St., Main Floor, must be provided. For absence due to religious
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Financial Mathematics I I CKMT 802

observance, visit http://www.ryerson.ca/senate/forms/relobservforminstr.pdf to obtain and submit the
required form.
PLAGIARISM
The Ryerson Student Code of Academic Conduct defines plagiarism and the sanctions against students
who plagiarize. All Chang School students are strongly encouraged to go to the academic integrity
website at www.ryerson.ca/academicintegrity and complete the tutorial on plagiarism.
ACADEMIC INTEGRITY
Ryerson University and The Chang School are committed to the principles of academic integrity as
outlined in the Student code of Academic conduct. Students are strongly encouraged to review the student
guide to academic integrity, including penalties for misconduct, on the academic integrity website at
www.ryerson.ca/academic integrity and the Student code of Academic conduct at
www.ryerson.ca/senate/policies.
RYERSON STUDENT EMAIL
All students in full and part-time graduate and undergraduate degree programs and all continuing
education students are required to activate and maintain their Ryerson online identity at
www.ryerson.ca/accounts in order to regularly access Ryerson’s E-mail (Rmail), RAMSS, my.ryerson.ca
portal and learning system, and other systems by which they will receive official University
communications.
COURSE REPEATS:
Senate GPA policy prevents students from taking a course more than three times. For complete GPA
policy see policy no. 46 at www.ryerson.ca/senate/policies.
RYERSON ACADEMIC POLICIES
For more information on Ryerson’s academic policies, visit the Senate website at www.ryerson.ca/senate.
Course Management Policy No. 145
Student Code of Academic conduct No. 60
Student code of non-Academic Conduct No. 61
Examination Policy No. 135
Policy on Grading, Promotion, and Academic Standing Policy No. 46
Undergraduate Academic consideration and Appeals Policy No. 134
Accommodation of Student Religious Observance Obligations Policy no. 150
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Financial Mathematics I I CKMT 802