**Stat 475 Mathematics and Statistics for Actuarial
Science I Syllabus**

**Instructor**: Dale Embers

**Office**: SEO 309

**email**: dembers@uic.edu

**Phone**: 312-413-2143

**Office Hours**: TBD

**Class Meeting**: M,W,F 3-3:50

**Location**: TH 204

**Text**: *Mathematics of Investment and Credit* (6th
Edition), Broverman and additional documents:

Duration
and Convexity

Interest Rate
Swaps

Determinants
of Interest Rates

**Course Description**: The focus of the course will be on
financial mathematics as it applies to actuarial science,
primarily centered on the SOA FM/ CAS Exam 2 material. Topics to
be included will be the valuation of cash flows and an
introduction to financial instruments. All of the desired Learning
Outcomes described by the SOA will be met.

**Grades**: The course grade is based on the total number of
points from hour exams, homework, and the final exam.

**Homework**: Homework will be assigned for each section
covered. The homework will be worth 100 points. Assigned Problems

**Exams**: The will be two exams during the course of the
semester. Each will be worth 100 points. The exams will be on 10/5
and 11/9.

**Final Exam**: The final exam will be cumulative and worth
200 points. The final exam is on Monday December 10th from
8:00-10:00 am.

**Prerequisite**: Grade of C or better in Math 210.

**Disability**: PolicyThe University of Illinois at Chicago is
committed to maintaining a barrier-free environment so that
students with disabilities can fully access programs, courses,
services, and activities at UIC. Students with disabilities who
require accommodations for access to and/or participation in this
course are welcome, but must be registered with the Disability
Resource Center (DRC). You may contact DRC at 312-413-2183 (v) or
312-413-0123 (TTY) and consult the following:
http://www.uic.edu/depts/oaa/disability_resources/faq/accommodations.html.

**Financial Mathematics**

The goal of the syllabus for 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 as a basis for future use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows.

The student will also be given an introduction to financial instruments, including derivatives, and the concept of no-arbitrage as it relates to financial mathematics.

Exam FM assumes a basic knowledge of calculus and an introductory knowledge of probability. The following learning objectives are presented with the understanding that students are allowed to use specified calculators on the exam. The education and examination of students reflects that fact. In particular, such calculators eliminate the need for students to learn and be examined on certain mathematical methods of approximation.

LEARNING OBJECTIVES

A. Time Value of Money (10-15%)

1. The student will be able to define and recognize the definitions of the following terms: interest rate (rate of interest), simple interest, compound interest, accumulation function, future value, current value, present value, net present value, discount factor, discount rate (rate of discount), convertible m-thly, nominal rate, effective rate, inflation and real rate of interest, force of interest, equation of value.

2. The student will 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 rate, the nominal interest rate convertible m-thly, the effective discount rate, the nominal discount rate convertible m-thly, or the force of interest, calculate any of the other items.

c. Write the equation of value given a set of cash flows and an interest rate.

B. Annuities/cash flows with payments that are not contingent (15-20%)

1. The student will be able to define and recognize the definitions of the following terms: annuity-immediate, annuity due, perpetuity, payable m-thly or payable continuously, level payment annuity, arithmetic increasing/decreasing annuity, geometric increasing/decreasing annuity, term of annuity.

2. For each of the following types of annuity/cash flows, given sufficient information of immediate or due, present value, future value, current value, interest rate, payment amount, and term of annuity, the student will be able to calculate any remaining item.

a. Level annuity, finite term

b. Level perpetuity

c. Non-level annuities/cash flows

i) Arithmetic progression, finite term

ii) Arithmetic progression, perpetuity

iii) Geometric progression, finite term

iv) Geometric progression, perpetuity

v) Other non-level annuities/cash flows

C. Loans (15-20%)

1. The student will 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.

2. The student will be able to:

a. Given any four of term of loan, interest rate, payment amount, payment period, principal, calculate the remaining item.

b. Calculate the outstanding balance at any point in time.

c. Calculate the amount of interest and principal repayment in a given payment.

d. Given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.

e. Perform similar calculations to a-d when refinancing is involved.

D. Bonds (15-20%)

1. The student will be able to define and recognize the definitions of the following terms: price, book value, amortization of premium, accumulation of discount, redemption value, par value/face value, yield rate, coupon, coupon rate, term of bond, callable/non-callable.

2. Given sufficient partial information about the items listed below, the student will be able to calculate the any of the remaining items.

a. Price, book value, amortization of premium, accumulation of discount

b. Redemption value, face value

c. Yield rate

d. Coupon, Coupon rate

e. Term of bond, point in time that a bond has a given book value, amortization of premium, or accumulation of discount

E. General Cash Flows and Portfolios (10-15%)

1. The student will be able to define and recognize the definitions of 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 (Macaulay and modified), portfolio, spot rate, forward rate, yield curve, stock price, stock dividend.

2. The student will be able to:

a. Calculate the dollar-weighted and time-weighted rate of return.

b. Calculate the duration and convexity of a set of cash flows.

c. Calculate either Macaulay or modified duration given the other.

d. Use duration to approximate the change in present value due to a change in interest rate. i. Using 1st-order linear approximation based on modified duration. ii. Using 1st-order approximation based on Macaulay duration.

e. Calculate the price of a stock using the dividend discount model.

F. Immunization (10-15%)

1. The student will be able to define and recognize the definitions of the following terms: cash flow matching, immunization (including full immunization), Redington immunization.

2. The student will be able to:

a. Construct an investment portfolio to fully immunize a set of liability cash flows.

b. Construct an investment portfolio to match present value and duration of a set of liability cash flows.

c. Construct an investment portfolio to exactly match a set of liability cash flows.

G. Interest Rate Swaps (0-10%)

1. The student will be able to define and recognize the definitions of the following

terms: swap rate, swap term or swap tenor, notional amount, market value of a swap,

settlement dates, settlement period, counterparties, deferred swap, interest rate

swap net payments.

2. The student will be able to calculate the swap rate in an interest rate swap, deferred

or otherwise, and with either constant or varying notional amount.

H. Determinants of Interest Rates (0-10%)

1. The student will be able to define and recognize the components of interest rates including: real risk-free rate, inflation rate, default risk premium, liquidity premium, and maturity risk premium.

2. The student will be able to explain how the components of interest rates apply in

various contexts, such as commercial loans, mortgages, credit cards, bonds,

government securities.

3. The student will be able to explain:

a. The impact of fiscal policy and monetary policy on interest rates.

b. The roles of the Federal Reserve and the FOMC in carrying out fiscal policy and monetary policy.

c. The tools used by the Federal Reserve and the FOMC including targeting the Federal Reserve rate, setting reserve requirements, setting the discount rate.

4. The student will be able to explain the factors affecting the yield curve including liquidity preference, opportunity cost, preferred habitat, and market segmentation.

5. The student will be able to explain how interest rates differ from one country to another (e.g., U.S. vs. Canada).