Course Code:                 MATH 2211

Course Title:                  Mathematics of Finance I

Course Type:                 Core

Level:                            2

Semester:                     1           

No. of Credits:               3

Prerequisite(s):              MATH 1141, MATH 1142,

                                      MATH 1151, MATH 1152

 

 Course Rationale

The aim of this course is to provide an understanding of the fundamental concepts of financial mathematics, and how those concepts are applied in calculating present and accumulated values for various streams of cash flows. These cash flows are viewed as a basis for future use in reserving, valuation, pricing, asset/liability management, investment income, capital budgeting and valuing contingent cash flows. The candidate will also be given an introduction to financial instruments.

 

Course Description

This course covers topics relevant in financial mathematics that include measurement of interest, accumulation and discount, forces of interest and discount, equations of value, annuities, perpetuities, amortization and sinking funds, yield rates, bonds and securities, depreciation, depletion, and capitalized costs.

Assessment is designed to encourage students to work continuously with the course materials. Active learning will be achieved through marked assignments supplemented by problem papers, allowing continuous feedback and guidance on problem solving techniques in tutorials and lectures. Assessment will be based on the marked assignments and in-course tests followed by a final examination based on the whole course. Software used in the actuarial field will be incorporated in the course so that students develop practical skills. 

 

Content

  • Introduction to actuarial science;
  • Measurement of interest;
  • Accumulation and discount
  • Forces of interest and discount;
  • Equations of value
  • Basic annuities;
  • Perpetuities
  • Yield rates.
  • Amortization schedule and sinking funds:
  • Bonds
  • Common stocks, preferred stocks and other securities Practical applications.

 Learning Outcomes

 On completion of these modules the student should be able to:

A. Introduction to Actuarial Science

  • Apply the basic techniques of actuarial mathematics and its application to insurance, pensions, banking etc.
  • Explain the role of actuarial mathematics in the world of finance.

B. Measurement of Interest

  • Define the following terms: interest rate (rate of interest), simple interest, compound interest, accumulation function, future value, present value/net present value, discount factor, discount rate (rate of discount), convertible m-thly, nominal rate, effective rate, force of interest and equation of value
  • Given any two of interest rate, present value, or future value, students will be able to calculate the third based on simple or compound interest.
  • Given any one of the effective interest rate, the nominal interest rate convertible m-thly, the effective discount rate, the nominal discount rate convertible m-thly, or the force of interest, students will be able to calculate all of the other items.
  • Write the equation of value given a set of cash flows and an interest rate.

C. Annuities

  • Define the following terms: annuity-immediate, annuity-due, perpetuity, payable m-thly, level payment annuity, arithmetic increasing/decreasing payment annuity, geometric increasing/decreasing payment annuity, and term of annuity
  • Given an annuity with level payments, immediate (or due), payable m-thly, and any three of present value, future value, interest rate, payment, and term,  calculate the remaining two items.
  • Given an annuity with non-level payments, immediate (or due), payable m-thly, the pattern of payment amounts, and any three of present value, future value, interest rate, payment amounts, and term of annuity, calculate the remaining two items. .

D. Loans

  • Define the following terms: principal, interest, term of loan, outstanding balance, final payment (drop payment, balloon payment), amortization, and sinking fund
  • Given any four of term of loan, interest rate, payment amount, payment period, principal, calculate the remaining items.
  • Calculate:
  • The outstanding balance at any point in time.
  • The amount of interest and principal repayment in a given payment.
  • Given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.

  E. Bonds and other Securities

  • Define the following terms: price, redemption value, par value/face value, coupon, coupon rate, term of bond, yield rate, callable/non-callable, book value, and accumulation of discount
  • Given any four of price, redemption value, yield rate, coupon rate, and term of bond, calculate the remaining item.

F. Yield Rates

  • Define the following terms: yield rate/rate of return, dollar-weighted rate of return/time-weighted rate of return, current value, duration (Macaulay and modified) , convexity, portfolio, spot rate, forward rate, yield curve, stock price, and stock dividend
  • Calculate the following:
  • Current value of a set of cash flows.
  • Portfolio yield rate.
  • Dollar-weighted and time-weighted rate of return.
  • Duration and convexity of a set of cash flows.
  • Either Macaulay or modified duration given the other
  • Price of a stock using the dividend discount model.

  G. Practical Applications

  • Calculate installments for:
  • Consumer loans;
  • Real estate mortgages;
  • Depreciation costs.

Cognitive skills, Core skills and Professional Awareness

  • Awareness of the principal statistical methods and models used in assessing problems in interest theory for actuarial work
  • Possession of the knowledge required to work in the area of finance in the actuarial context
  • Application of the appropriate and rigorous use of mathematical modeling to formulate workable solutions to important financial problems

Teaching Methodology

 

Lectures:          Three lectures per week (50 minutes each)

Tutorial:           One weekly tutorial session (50 minutes), based on material covered during lectures.

 

Assessment Criteria

Mathematics of Finance is assessed by combination of coursework (50%) and a single 2-hour written exam at the end of the semester (50%).

 

Assessment:                    In-course Tests                                       30%

                                       Assignments and Quizzes                       20%

                                       Final Exam                                             50%

 

In-course Tests:           Two 50-minute written papers (15% each) consisting of compulsory questions of varying length

 

Assignments:    Two papers to be submitted: One paper on the first part of the course and the other on the second part of the course. Each assignment is worth 4%. Tutorial practice papers will be given every week to be handed in the next week. Tutorial papers are not graded as part of the course work.

 

QUIZZES:                     Six quizzes worth 2% each.

Exam Format:             One two-hour written paper with compulsory questions.

 

 Course Calendar

 

Week

Topic to be taught

Assessment

 

1

Introduction /Course Overview

Introduction to actuarial science, measurement of interest

 

Tutorial #1 is given

2

Accumulation and discount

Tutorial #2 is given and Tutorial #1 is corrected

3

Forces of interest and discount

Tutorial #3 is given and Tutorial #2 is corrected

4

Equations of value, basic annuities

Tutorial #4 is given and Tutorial #3 is corrected

5

Basic annuities, Perpetuities

First coursework test is given

6

Yield rates

Tutorial #5 is given and Tutorial #4 is corrected. Assignment #1 is given

7

Amortization schedules and sinking funds

Tutorial #6 is given and Tutorial #5 is corrected

8

Bonds

Tutorial #7 is given and Tutorial #6 is corrected

9

Duration

Tutorial #8 is given and Tutorial #7 is corrected

10

 Immunization

Second coursework test is given

11

Common stocks, preferred stocks and other securities

Tutorial #9 is given and Tutorial #8 is corrected. Assignment #2 is given.

12

Practical applications

Tutorial #10 is given and Tutorial #9 is corrected

13

Revision

Revision

                                                                                   

Required Readings

 

The prescribed text is “The Theory of Interest” by Stephen G. Kellison 3rd Edition 2008.

Additional Readings

Other recommended texts that students may find useful are:

  • Mathematics of Investment and Credit – Samuel A. Broverman 4th Edition 2008
  • Mathematical Interest Theory – Daniel & Vaaler 2009
  • Schaum’s Outline:Mathematics of Finance –Petr Zima, Robert L. Brown 2nd Edition 1996.