Spring 2014
THE CHINESE UNIVERSITY OF HONG KONG
FINA 2210 B/C Interest Theory and Finance
Assignment No. 1 (for Chapter 1)
Deadline: 7 February 2014 (5:00pm Sharp)
1. Assume that a(t) = ln(0.5t2 + e) + 0.05t0.3 ,
(a) nd i2 and i3 .
(b) nd d3 and d4 .
(c)
Exam FM November 2005
1.
An insurance company earned a simple rate of interest of 8% over the last calendar year based on the following information:
Assets, beginning of year Sales revenue Net investment income Salaries paid Other expenses paid
25,000,000
I.
Introduction:
A derivative is a financial instrument that has a value determined by an underlying asset.
Uses of derivatives:
o Risk management
o Speculation on prices
o Reducing transaction costs
o Avoiding taxes (regulatory arbitrage)
Financial en
Financial Mathematics ExamFebruary 2014
The Financial Mathematics exam is three-hour exam that consists of 35 multiple-choice questions and is
administered as a computer-based test. For additional details, please refer to Exam Rules
The goal of the syllab
I.
Interest Rate Measurement:
Accumulation Function, a(t): Accumulated value @ time (t) of an original investment of $1 Amount Function, A(t): Accumulated value @ time (t) of an original investment of $K
( )= ( )
Effective Rate of Interest, Effective Ra
Financial Mathematics
December 16, 2013
1
1.1
The Measurement of Interest
Accumulation function
a(t) a(t 1)
a(t 1)
A(t) A(t 1)
it =
A(t 1)
A(t) = k a(t)
it =
Under simple interest
a(t) = 1 + it
i
it =
1 + i(t 1)
Under compound interest
a(t) = (1 + i)t
1
P
Call and Put Options
Position
Long (Synthetic)
Forward
Bull Spread
Bear Spread
Ratio Spread
Collar
Straddle
Strangle
Written Straddle
Butterfly Spread
Asymmetric Butterfly
Spread
Reason for Taking
Profit Diagram
Payoff Diagram
(?)
Exam FM Formula Summary
Version 2.01
no driver
11/14/2006
Introduction
Since ASM does not have a formula summary, I decided to compile one to use as I started working on
old test questions. In the interest of other actuarial students, I thought I would sh
Basic stuff
= f (i ) =
1
d
i = f (d ) =
1 d
i
d = f (i ) =
1+ i
= f (d ) = 1 d
d = f ( ) = 1
1
1 +i
i = f ( ) =
Some combinations of basic equations
i d = id
11
=1
di
i = d
Nominal rates
m
i(m)
1 + i = 1 +
m
1
i m = m (i + 1) m 1
m
d (m)
1 d = 1
Basic stuff
= f (i ) =
i = f ( ) =
i = f (d ) =
d = f (i ) =
= f (d ) =
d = f ( ) =
Some combinations of basic equations
id =
11
=
di
i =
Nominal rates
1+ i =
im =
1 d =
dm =
Force of interest
t = f ( a (t ) ) =
a (t ) = f ( t ) =
const =
Annuities
a =
Exam FM/2 Interest Theory Formulas
by (/iropracy
This is a collaboration of formulas for the interest theory section of the SOA Exam FM / CAS Exam 2.
This study sheet is a free non-copyrighted document for students taking Exam FM/2.
The author of this stu
CLs Handy
Formula Sheet
(Useful formulas from Marcel Finans FM/2 Book)
Compiled by Charles Lee
8/19/2010
Interest
Interest
Simple
Compound
Discount
Simple
Compound
The Method of Equated Time
a(t)
Period
when
greater
Interest Formulas
Force of Interest
The
SOCIETY OF ACTUARIES
EXAM FM
FINANCIAL MATHEMATICS
EXAM FM SAMPLE QUESTIONS
This page indicates changes made to Study Note FM-09-05.
January 14, 2014:
Questions and solutions 5860 were added.
Copyright 2013 by the Society of Actuaries.
Some of the questio
Discount rate as function of interest rate
d=
=
Discount function under compound discount
a-1(t)=
=
Accumulation Factor in terms of a(t)
1+it=
Definition of effective rate of interest for nth period in terms of a(t)
in=
Definition of effective rate of dis
Spring 2014
THE CHINESE UNIVERSITY OF HONG KONG
FINA 2210 B/C Interest Theory and Finance
Assignment No. 2 (for Chapter 2 (Part A & B)
Deadline: February 28, 2014 (5:00pm Sharp)
1.
A family wishes to accumulate $250,000 in a college fund at the end of 18
Spring 2014
THE CHINESE UNIVERSITY OF HONG KONG
FINA2210 B/C Interest Theory and Finance
Assignment No. 3 (for Chapters 3, 4 and 5)
Deadline: 28 March 2014 (5:00pm Sharp)
1. You are given the following information: iS = 2.2%, iF = 2.7%, iS = 3.2% and iF =
Spring 2014
THE CHINESE UNIVERSITY OF HONG KONG
FINA2210 B/C Interest Theory and Finance
Assignment No. 4 (for Chapters 6, 7 and 8)
Deadline: 14 April 2014 (5:00pm Sharp)
* This is the LAST assignment for the course *
1. An investor buys two 20-year bonds
Period is the unit in which time is measured, e.g.
month, quarter, and year.
2
day,
Principal is the initial amount of money (capital) borrowed
or invested.
Interest is the compensation that a borrower of capital pays
to a lender of capital for its use
Chapter 2 - PART A:
Basic Annuities
January 11, 2014
Chapter 2 (Part A): Basic Annuities
A. Introduction
1. Denition
An annuity is dened as a series of payments made at equal
intervals of time.
An annuity-certain means that payments are certain to be
ma
Chapter 2 (Part B)
More General Annuities
January 17, 2014
Chapter 2 (Part B): More General Annuities
A. Payment period dierent from interest period
1. Payment period is longer than interest period
Illustration 1:
Given that j1 = 1% (eective rate of inter
Chapter 3
Spot Rates, Forward Rates and
the Term Structure
January 23, 2014
Chapter 3: Spot Rates, Forward Rates and the Term Structure
Learning Objectives
1. Spot rate of interest
2. Forward rate of interest
3. Yield curve
4. Term structure of interest r
Chapter 5
Loans and Costs of Borrowing
February 19, 2014
Chapter 5: Loans and Costs of Borrowing
Learning Objectives
1. Loan balance: prospective method and retrospective method
2. Amortization schedule
3. Sinking fund
4. Varying installments and varying
Chapter 6
Bonds and Bond Pricing
March 9, 2014
Chapter 6: Bonds and Bond Pricing
Learning Objectives
1. Types, features and risks of bond investments
2. Formulas for pricing a bond
3. Construction of bond amortization schedules
4. Pricing a bond between t
Chapter 7
Bond Yields and the Term Structure
March 18, 2014
Chapter 7: Bond Yields and the Term Structure
Learning Objectives
1. Yield to maturity, yield to call and par yield
2. Realized compound yield and horizon analysis
3. Estimation of the yield curv
Chapter 8
Bond Management
March 18, 2014
Chapter 8: Bond Management
Learning Objectives
1. Macaulay duration and modied duration
2. Duration and interest-rate sensitivity
3. Convexity
4. Some rules for duration calculation
5. Asset-liability matching and
T HE T H EO R Y O F I N TER ES T
SECOND EDIITIION SECOND ED T ON
STEPHEN G. KELLISON
READING NOTES
WEDNESDAY, SEPTEMBER 27, 2006 WEDNESDAY SEPTEMBER 27 2006
KELLISON'S READING NOTES TABLE OF CONTENTS
Chapter 1 The Measurement of Interest.4 1.1 Introductio