# Math 177: General Course Outline

## Catalog Description

177. Theory of Interest and Applications.(4). Lecture, three hours; discussion, one hour. Requisite: course 32B. Types of interest, time value of money, annuities and similar contracts, loans, bonds, portfolios and general cash flows, rate of return, term structure of interest rates, duration, convexity and immunization, interest rate swaps, financial derivatives, forwards, futures, and options. Letter grading.

## Course Information:

An introductory course on financial mathematics, Math 177 lays the foundation and prepares students for the series of courses required for the Financial Actuarial Mathematics major. By the end of this course, students should be familiar with numerous foundational concepts of financial mathematics, especially those from the theory of interest rates. Since one goal of the course is to help students prepare for the challenging Financial Mathematics (FM) exam) for the Society of Actuaries (SOA), two lectures before the midterms will be devoted to analysis of complex FM exam problems. While the basic ideas are mathematically elementary, their applications can be complex. The class is suitable for students who seek a career in financial engineering, the actuarial field, banking, etc., or are seeking to improve their financial literacy in a highly quantitative way.

## Textbook

Broverman, Samuel A. Mathematics of Investment and Credit. 7th ed., Actex Publications, 2017.

Bean, Michael A. (FSA, CERA FCIA, FCAS, PHD). Determinants of Interest Rates. Society of Actuaries, 2017. Education and Examination Committee of the Society of Actuaries - Financial Mathematics Study Note.
https://www.soa.org/Files/Edu/2017/fm-determinants-interest-rates.pdf

Alps, Robert (ASA, MAAA). Using Duration and Convexity to Approximate Change in Present Value. Society of Actuaries, 2017. Education and Examination Committee of the Society of Actuaries - Financial Mathematics Study Note.
https://www.soa.org/Files/Edu/2016/edu-2016-fm-24-17-using-duration-conv...

Beckley, Jeffrey (FSA, MAAA). Interest Rate Swaps. Society of Actuaries, 2017. Education and Examination Committee of the Society of Actuaries - Financial Mathematics Study Note.
Https://www.soa.org/Files/Edu/2017/fm-interest-rate-swaps.pdf

## Schedule of Lectures

Lecture Section Topics

1

Intro, 1.0-1.4

Simple, compound, nominal and effective interest rates. Accumulation. Equation of value, actuarial notation.

2

1.5, 1.6

Effective and nominal discount rates, force of interest.

3

Determinants of interest rates.

4

2.1

Level payment annuities.

5

2.2, 2.3

Non-constant payments and other generalizations.

6

2.4

Yield and reinvestment rates, depreciation.

7

3.1, 3.2

Amortization of loans.

8

4.1, 4.2

Determination of bond prices and amortization of a bond.

9

4.3, 4.4

Examples of bonds and applications.

10

5.1

Internal rate of return defined and net present value.

11

5.2, 5.3

Other methods (dollar-weighted and time weighted) and examples of rate of return.

12

Review/Leeway.

13

Advanced problem analysis from Weeks 1-4.

14

Advanced problem analysis from Weeks 1-4.

15

Midterm

16

6.1, 6.2

Basic definitions, spot rates.

17

6.3

Forward rates.

18

6.4

Applications and examples of arbitrage, forward rate agreements and at-par yield.

19

7.1.1-7.1.2

Macaulay duration and modified duration.

20

7.1.3-7.1.5, 7.2

Application to valuation of cash flows, dependence on term structure.

21

7.2

Convexity and immunization.

22

Definitions, determining swap rate.

23

Case of constant notional amount, net payments.

24

Market value of a swap.

25

Advanced problem analysis from Weeks 6-8.

26

Advanced problem analysis from Weeks 6-8.

27

Midterm

28

9.1-9.4

Derivatives, dividend discount model, short sale of stock, equity investments, financial derivatives.

29

9.5

Forward contracts.

30

9.6, 10.1-10.2

Futures, options.