Course Title:
Financial MathematicsCourse Code:
MTH3602Program:
BSc. in MathematicsDepartment:
MathematicsCollege:
Jamoum University CollegeInstitution:
Umm Al-Qura University2
Table of Contents
A. Course Identification ... 3
6. Mode of Instruction (mark all that apply) ... 3
B. Course Objectives and Learning Outcomes ... 3
1. Course Description ... 3
2. Course Main Objective ... 3
3. Course Learning Outcomes ... 3
C. Course Content ... 5
D. Teaching and Assessment ... 6
1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods ... 6
2. Assessment Tasks for Students ... 7
E. Student Academic Counseling and Support ... 7
F. Learning Resources and Facilities ... 7
1.Learning Resources ... 8
2. Facilities Required ... 8
G. Course Quality Evaluation ... 8
H. Specification Approval Data ... 9
3
A. Course Identification
1. Credit hours: 4 2. Course type
a. University College Department ✓ Others
b. Required Elective ✓
3. Level/year at which this course is offered:
4. Pre-requisites for this course (if any):
لماكتلا باسح 5. Co-requisites for this course (if any):
Not applicable
6. Mode of Instruction (mark all that apply)
No Mode of Instruction Contact Hours Percentage
1 Traditional classroom Four hours/week %100
2 Blended 0 0
3 E-learning 0 0
4 Distance learning 0 0
5 Other 0 0
7. Contact Hours (based on academic semester)
No Activity Contact Hours
1 Lecture 40
2 Laboratory/Studio 0
3 Tutorial 0
4 Others (specify) 0
Total 40
B. Course Objectives and Learning Outcomes
1. Course DescriptionFinancial Mathematics will provide students an introduction to provide students with a solid
foundation in numerical models used to value financial securities and assess risk. Topics include time value of money, annuities and cash flows, loans, bonds, general cash flows and portfolios,
immunization, and swaps.
2. Course Main Objective
To provide an understanding of the basic concepts of financial mathematics and the application of these concepts in calculating present and cumulative values for various streams of cash flows as a basis for future use in the following areas: Reserving, Valuation, Pricing, Asset/Liability Management, Investment Income, Capital Budgeting, and Valuation of Contingent Cash Flows.
3. Course Learning Outcomes
CLOs Aligned
PLOs
4
CLOs Aligned
PLOs 1 Knowledge and understanding
1.1 To be able to:
a. Given any three of interest rate, period
of time, present value, current value, and future value, calculate the remaining item using simple or compound interest. Solve time value of money equations involving variable force of interest.
b. Given any one of the effective interest rates, the nominal interest rate the effective discount rate, the nominal discount, or the force of
interest.
1.2 To be able to define and recognize the definitions of annuity-
immediate, annuity due, perpetuity, level payment annuity, arithmetic annuity, geometric annuity.
1.3 To be able to define and recognize the definitions of the following terms: principal, interest, term of loan, outstanding balance, final payment (drop payment, balloon payment), amortization, sinking fund.
1.4 To be able to define and recognize the definitions of the following terms: term of loan, Outstanding balance, final payment (drop payment, balloon payment).
1.5 To be able to define and recognize the definitions of the following terms: securities, price of the bond, redemption value, par value/face value, yield rate, coupon, coupon rate, term of bond, book value, amortization of premium, accumulation of discount, callable.
1.6 To be able to define and recognize the definitions of the following terms: Measuring the rate of return of an investment (Yield rate, Dollar- weighted rate of return, Time-weighted rate of return), and Interest rate sensitivity (Duration” Macaulay and modified”, convexity
“Macaulay and modified”)
1.7 To be able to define and recognize the definitions of the following terms: Asset -Liability Matching and Immunization (Redington immunization, full immunization)
1.8 To be able to define and recognize the definitions of the following terms: Definitions of swap rate, swap term or swap tenor, notional amount
2 Skills :
2.1 Report the value equation given a set of cash flows and an interest rate.
2.2 Give sufficient information of immediate or due, present value, future value, current value, interest rate, payment amount, and term of annuity, the candidate will be able to calculate any remaining item.
2.3 To be able to find any four of term of loan, interest rate, payment amount, payment period, principal, finding the remaining item.
To be able to calculate the outstanding balance at any point in time. Also, To be able to given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.
2.4 To be able to calculate the value of book value, amortization of premium, accumulation of discount, Redemption value, face value, Yield rate, Term of bond, point in time that a bond has a given book value, amortization of premium, or accumulation of discount.
2.5 To be able to calculate the dollar-weighted and time- weighted rate of return
5
CLOs Aligned
PLOs and calculate the duration and convexity of a set of cash flows.
2.6 To be able to construct an investment portfolio to fully immunize, to match present value and duration, and portfolio to exactly match the set of liability cash flows.
2.7 To be able to calculate the swap rate in an interest rate swap, deferred or otherwise, and with either constant or varying notional amount.
3 Values:
3.1 Prepare for success in disciplines that rely on Financial Mathematics and in more advanced financing which incorporate these topics, such as Time Value of Money, Annuities, Loans, and Bonds
Develop connections within branches of Financial Mathematics and between arithmetic Integration, Probability, and other disciplines.
3.2 Apply scientific models and tools effectively.
3.3 Apply knowledge gained during the course using computer applications 3... show the ability to work independently and within groups
C. Course Content
No List of Topics Contact
Hours
1
Brief reminder of the underlying mathematics.
a. Geometric series and sum, b. derivatives and integrals,
c. Maclaurin series for exponentials.
2
2
Time value of money or measurement of interest
a. The concept of simple interest and the factors affecting the determination of the value of interest, Maturity, or accumulated value.
b. compound interest and the basic concepts of long-term investing.
c. Interest rate, effective rate, nominal rate, and force rate of discount, varying interest, and inflation of interest
6
3
Annuities:
a. Annuity -immediate b. Annuity- due
c. Annuity value any date d. Perpetuities
e. Varying annuities
f. Annuity whose payment form a geometric progression g. Annuity whose payment form an arithmetic progression.
8
4
Loan repayments a. term of loan.
b. Outstanding balance, final payment (drop payment, balloon payment).
c. Amortization schedule. 4
5 Bonds and securities valuations.
a. Type of securities 8
6
b. Price of the bond, redemption value, par value/face value, yield rate, coupon, coupon rate, term of bond
c. book value, amortization of premium, accumulation of discount, d. callable.
6
Measuring the rate of return of an investment a. Yield rate,
b. Dollar-weighted rate of return, c. Time-weighted rate of return.
Interest rate sensitivity
a. Duration (Macaulay and modified), b. convexity (Macaulay and modified)
4
7
Asset -Liability Matching and Immunization a. Redington immunization
b. full immunization 4
8
Interest Rate Swaps
a. Definitions: swap rate, swap term or swap tenor, notional amount, deferred swap
b. General Formula: spot interest rate, forward rate, c. Special Formula
d. Net payment, market value of a swap,
4
Total
D. Teaching and Assessment
1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods
Code Course Learning Outcomes Teaching Strategies Assessment Methods 1.0 Knowledge and understanding
1.1
To be able to:
a. Given any three of interest rate, period of time, present value, current value, and future value, calculate the remaining item using simple or compound interest. Solve time value of money equations involving variable force of interest.
b. Given any one of the effective interest rates, the nominal interest rates the effective discount rate, the nominal discount, or the force of interest.
Lectures Tutorials Discussion Problem Solving
group work
Exams Home work.
1.2
To be able to define and recognize or evaluate the Time Value of Money, Annuities, Loans, and Bonds.
1.3
To be able to define and recognize the definitions of the following terms:
Definitions of swap rate, swap term or swap tenor, notional amount
2.0 Skills
2.1 Report the value equation given a set of Lectures Exams
7
Code Course Learning Outcomes Teaching Strategies Assessment Methods cash flows and an interest rate. Tutorials
Solve Problem Brain Storming
group work
Quizzes.
Homework.
Discussion 2.2
Give sufficient information of immediate or due, present value, future value, current value, interest rate, payment amount, and term of annuity, the candidate will be able to calculate any remaining item.
2.3
To be able to find any four of term of loan, interest rate, payment amount, payment period, principal, finding the remaining item.
To be able to calculate the outstanding balance at any point in time. Also, To be able to given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.
3.0 Values
3.1
Prepare for success in disciplines that rely on Financial Mathematics and in more advanced financing which incorporate these topics, such as Time Value of Money, Annuities, Loans, and Bonds
Lectures Tutorials Solve Problem Brain Storming
group work
Exams Quizzes.
Homework.
Discussion 3.2
Develop connections within branches of Financial Mathematics and between arithmetic Integration, Probability, and other disciplines.
2.3 Apply scientific models and tools effectively.
2. Assessment Tasks for Students
# Assessment task* Week Due Percentage of Total
Assessment Score
1 Midterm exam Sixth week %25
2 Quizzes and HomeWorks During semester %25
3 Final exam End of semester %50
*Assessment task (i.e., written test, oral test, oral presentation, group project, essay, etc.)
E. Student Academic Counseling and Support
Arrangements for availability of faculty and teaching staff for individual student consultations and academic advice:
All faculty members are required to be in their offices outside of class hours. Each member will provide at least 4 hours per week to give academic advice to students and to better explain concepts covered in lectures. Students are required to complete homework assignments. Students are welcome to work together on the homework. However, each student must turn in their own assignments, and students are not allowed to copy from another student's work. Deadline extensions for homework will not be granted. Students are encouraged to talk to the professor about homework problems.
F. Learning Resources and Facilities
8
1.Learning Resources Required Textbooks
Vaaler, L.J.F., Harper, S.K., and Daniel, J.W. Mathematical Interest Theory (Third Edition), 2019, The Mathematical Association of America, ISBN: 978- 1-4704-4393-1
Essential References Materials
Kellison, S.G., The Theory of Interest (Third Edition), 2009, Irwin/McGraw- Hill, ISBN: 125921544X or 978-1259215445
Electronic Materials Broverman, S.A., Mathematics of Investment and Credit (Seventh Edition), 2017, ACTEX Publications, ISBN 978-1-63588-221-6
Other Learning Materials
Francis, J. and Ruckman, C., Interest Theory – Financial Mathematics and Deterministic Valuation; (Second Edition), 2018, ActuarialBrew, ISBN 978- 0998160412
Chan, Wai-Sum, and Tse, Yiu-Kuen, Financial Mathematics for Actuaries, Second Edition, 2018, World Scientific Publishing Company, ISBN: 978- 9813224667 (hard cover) or 978-9813224674 (paperback).
ADDITIONAL REFERENCES :
o FM-25-17 Interest Rate Swaps
o FM-24-17 Using Duration and Convexity to Approximate Change in Present Value
o Notation and terminology used for Exam FM o FM-26-17 Determinants of Interest Rates.
2. Facilities Required
Item Resources
Accommodation
(Classrooms, laboratories, demonstration rooms/labs, etc.)
Large classrooms that can accommodate more than 30 students
Technology Resources
(AV, data show, Smart Board, software, etc.)
Data Show, Smart Board Other Resources
(Specify, e.g. if specific laboratory equipment is required, list requirements or
attach a list)
None
G. Course Quality Evaluation
Evaluation
Areas/Issues Evaluators Evaluation Methods
Effectiveness of teaching and assessment
Students Direct
Quality of learning resources Students Direct Extent of achievement of
course learning outcomes
Faculty Member Direct
Effectiveness of teaching and assessment
Students Direct
Evaluation areas (e.g., Effectiveness of teaching and assessment, Extent of achievement of course learning outcomes, Quality of learning resources, etc.)
9
Evaluators (Students, Faculty, Program Leaders, Peer Reviewer, Others (specify) Assessment Methods (Direct, Indirect)
H. Specification Approval Data
Council / Committee Council of the Mathematics Department
Reference No.
Date
