Math 494 Financial Mathematics Syllabus

Instructor: Dale Embers
Office: SEO 309
Email: dembers@uic.edu
Phone: 3-2143
Office Hours: M,W,F 12-3
Class Meeting: M,W,F 3-3:50
Location: LC A2
Text: Mathematics of Investment and Credit (5th Edition), Broverman.

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 are at the link below.  The site will be updated with due dates as the course progresses.
Assigned Homework Problems

Exams: The will be two exams during the course of the semester.  Each will be worth 100 points.  The exams will be on 2/17 and 3/30

Final Exam:  The final exam will be cumulative and worth 200 points.  The final will be Monday, April 30th from 8-10 am.

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

LEARNING OBJECTIVES

I. Interest Theory

A. Time Value of Money

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Interest rate (rate of interest)

b. Simple interest

c. Compound interest

d. Accumulation function

e. Future value

f. Present value/net present value

g. Discount factor

h. Discount rate (rate of discount)

i. Convertible m-thly

j. Nominal rate

k. Effective rate

l. Force of interest

m. Equation of value

2. The candidate will be able to:

a. Given any two of interest rate, present value, or future value, calculate the third based

on simple or compound 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 all of the other items.

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

B. Annuities with payments that are not contingent

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Annuity-immediate

b. Annuity-due

c. Perpetuity

d. Payable m-thly

e. Level payment annuity

f. Arithmetic increasing/decreasing payment annuity

g. Geometric increasing/decreasing payment annuity

h. Term of annuity

2. The candidate will be able to:

a. 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.

b. 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.

C. Loans

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Principal

b. Interest

c. Term of loan

d. Outstanding balance

e. Final payment (drop payment, balloon payment)

f. Amortization

g. Sinking fund

2. The candidate will be able to:

a. Given any four of term of loan, interest rate, payment amount, payment period,

principal, calculate the remaining items.

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.

D. Bonds

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Price

b. Redemption value

c. Par Value/Face value

d. Coupon, Coupon rate

e. Term of bond

f. Yield rate

g. Callable/non-callable

h. Book value

i. Accumulation of discount

2. The candidate will be able to:

a. Given any four of price, redemption value, yield rate, coupon rate, and term of bond,

calculate the remaining item.

E. General Cash Flows and Portfolios

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Yield rate/rate of return

b. Dollar-weighted rate of return/Time-weighted rate of return

c. Current value

d. Duration (Macaulay and modified)

e. Convexity

f. Portfolio

g. Spot rate

h. Forward rate

i. Yield curve

j. Stock price, stock dividend

2. The candidate will be able to:

a. Calculate the current value of a set of cash flows.

b. Calculate the portfolio yield rate.

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

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

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

f. Use duration and convexity to approximate the change in present value due to a change

in interest rate.

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

F. Immunization

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Cash-flow matching;

b. Immunization (including full immunization);

c. Redington immunization.

2. The candidate 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.

II. Financial Economics

A. General Derivatives

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Derivative, Underlying asset, Over-the-counter market

b. Ask price, Bid price, Bid-ask spread

c. Short selling, Short position, Long position

d. Stock index

e. Spot price

f. Net profit/payoff

g. Credit risk

h. Marking-to-market

i. Margin, Maintenance margin, Margin call

2. The candidate will be able to evaluate an investor's margin position based on changes in asset values.

B. Options

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Call option, Put option

b. Expiration, Expiration date

c. Strike price/Exercise price

d. European option, American option, Bermudan option

e. In-the-money, At-the-money, Out-of-the-money

f. Covered call, Naked writing

g. Dividends

h. Put-call parity

2. The candidate will be able to evaluate the payoff and profit of basic derivative contracts.

C. Hedging and Investment Strategies

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Hedging, Arbitrage

b. Diversifiable risk, Nondiversifiable risk

c. Synthetic forwards

c. Spreads (including bull, bear, box, and ratio spreads)

d. Collars (including zero-cost collars), Paylater strategy

e. Straddles (including strangles, written straddles and butterfly spreads)

f. Convertible bond, Mandatorily convertible bond

2. The candidate will be able to:

a. Explain how derivative securities can be used as tools to manage financial risk.

b. Explain the reasons to hedge and not to hedge.

c. Evaluate the payoff and profit of hedging strategies.

D. Forwards and Futures

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Forward contract, Prepaid forward contract

b. Outright purchase, Fully leveraged purchase

c. Implied repo rate

d. Cost of carry

e. Lease rate

f. Futures contract

2. The candidate will be able to:

a. Determine forward price from prepaid forward price.

b. Explain the relationship between forward price and futures price.

c. Explain the relationship between forward price and future stock price.

d. Use the concept of no-arbitrage to determine the theoretical value of futures andforwards.

e. Given any four of call premium, put premium, forward price, strike price and interestrate, calculate the remaining item using the put-call parity formula.

E. Swaps

1. The candidate will be able to define and recognize the definitions of the following terms:

a. Swap, Prepaid swap

b. Swap term, Swap spread, Notional Amount

c. Simple commodity swap, Interest rate swap

d. Deferred swap