Financial Mathematics: Weeks 7 & 8
Financial Mathematics
Benjamin Avanzi1
1 University of New South Wales
Actuarial Studies, Australian School of Business
b.avanzi@unsw.edu.au
Weeks 7 & 8
1/58
Financial Mathematics: Weeks 7 & 8
Plan
Non-arbitrage pricing

ACTL2001 Support Class Week 8 Exercises
Term Structure of Interest Rates
1.
[IoA Exam CT1 April 2005 Q9]
The one-year forward rate of interest at time t 1 year is 5% per annum effective.
The gross redemption yield of a two-year fixed interest stock issu

ACTL2001 Support Class Week 4 Exercises
Annuities
1.
Consider a university scholarship which offers the following payments to a student:
$6,000 per annum paid semi-annually in arrears for the first year;
$9,000 per annum paid quarterly in arrears for th

ACTL2001 Support Class Week 12 Exercises
Stochastic Return Models
1.
[IoA Exam CT1 September 2008 Q6] A pension fund holds an asset with current value $1 million.
The investment return on the asset in a given year is independent of returns in all other ye

ACTL2001 Support Class Week 9 Exercises
Options
1.
[UNSW Final Exam 2004 Q10(ii)] In a one period binomial model, it is assumed that the current
share price of 260 will either increase to 285 or decrease to 250 with equal probability at the end of
one yea

ACTL2001 Support Class Week 10 Exercises
Price Sensitivity and Redington Immunisation
1.
[UNSW Final Exam 2007 Q8] A fund must make payments of $50,000 at the end of the sixth and
eight years as liabilities. The fund manager wants to immunise the interest

ACTL2001 Support Class Week 11 Exercises
Life Insurance Mathematics
1.
[UNSW Final Exam 2007 Q9] Assume that each of 100 independent lives is of age x . Each individual
is subject to a constant force of mortality, 0.04 . Each individual is insured for a d

ACTL2001 Support Class Week 3 Exercises
Cash Flow Models
1.
Bob is going to receive $250, $500 and $750 at the end of years 1, 2 and 3 respectively. Draw a cash
flow diagram of the cash flows. Determine the present value of the cash flows at an annual
eff

Students will be able to apply critical thinking and analytical skills to solve actuarial problems.
Criterion
Critical Thinking and Analytical Skills to solve actuarial problems
Analysis of the task
Apply appropriate theory and logic to interpret and solv

Australian School of Business
School of Actuarial Studies
Financial Mathematics
Exercises
S1 2012
17 March 2012
Contents
1 Time Value of Money and Cash Flow Valuation
1.1
2
Time Value of Money . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Exerci

Financial Mathematics
Financial Mathematics
Benjamin Avanzi1
1 University of New South Wales
Actuarial Studies, Australian School of Business
b.avanzi@unsw.edu.au
Module 4: Interest Rate Risk
Section 9: Immunisation: Example
1/6
Financial Mathematics
Thes

Financial Mathematics
Financial Mathematics
Benjamin Avanzi1
1 University of New South Wales
Actuarial Studies, Australian School of Business
b.avanzi@unsw.edu.au
Module 4: Interest Rate Risk
Section 8: Immunisation
1/10
Financial Mathematics
These topic

Financial Mathematics
Financial Mathematics
Benjamin Avanzi1
1 University of New South Wales
Actuarial Studies, Australian School of Business
b.avanzi@unsw.edu.au
Module 4: Interest Rate Risk
Section 7: Fisher-Weil Duration and Convexity
1/4
Financial Mat

Financial Mathematics
Financial Mathematics
Benjamin Avanzi1
1 University of New South Wales
Actuarial Studies, Australian School of Business
b.avanzi@unsw.edu.au
Module 4: Interest Rate Risk
Section 6: Practical Considerations
1/9
Financial Mathematics
T

Financial Mathematics
Financial Mathematics
Benjamin Avanzi1
1 University of New South Wales
Actuarial Studies, Australian School of Business
b.avanzi@unsw.edu.au
Module 4: Interest Rate Risk
Section 5: Measures of Interest Sensitivity
1/9
Financial Mathe

ACTL2001 Support Class Week 6 Exercises
Loans and Fixed Interest Securities
1.
[Broverman 3.1.7] A 30-year loan of 1,000 is repaid with payments at the end of each year. Each of
the first ten payments equals the amount of interest due. Each of the next te

8. Options
Options give an investor the choice of buying or selling an asset in the future.
European options can only be utilised at the time of maturity, whereas American options can be
utilised before or at the time of maturity. In this course, only Eur

9. Stochastic Return Models
9.1 Stochastic Processes
In the course so far, we have assumed that interest rates are fixed into the future i.e. deterministic.
In reality, interest rates are random and they need to be modelled using a stochastic process,
whi

Financial Mathematics: Week 9
Financial Mathematics: Week 9
Plan
Sensitivity of price to interest
In a nutshell
Duration of bonds
Convexity of bonds
Numerical Approximation
Fisher-Weil duration and convexity
Financial Mathematics
Benjamin Avanzi1
1 Univer

Financial Mathematics: Weeks 11 & 12
Financial Mathematics: Weeks 11 & 12
Plan
Introduction to stochastic returns
Financial Mathematics
General formulas in case of iid returns
Bernard
Wong1
Accumulation of an annuity
1 University
of New South Wales
Actuar

Financial Mathematics: Week 10
Financial Mathematics: Week 10
Plan
Introduction
History
Financial Mathematics
Benjamin
The future lifetime of a life aged x
Survival probabilities
Discrete time
Avanzi1
1 University of New South Wales
Actuarial Studies, Aus

Financial Mathematics: Weeks 11 & 12
Financial Mathematics
Bernard Wong1
1 University of New South Wales
Actuarial Studies, Australian School of Business
bernard.wong@unsw.edu.au
Weeks 11 & 12
1/39
Financial Mathematics: Weeks 11 & 12
Plan
Introduction to

Financial Mathematics: Weeks 7 & 8
Financial Mathematics: Weeks 7 & 8
Plan
Non-arbitrage pricing
Financial Mathematics
The term structure of interest
Benjamin Avanzi1
Derivatives
1 University
of New South Wales
Actuarial Studies, Australian School of Busi

Financial Mathematics: Week 6
Financial Mathematics
Benjamin Avanzi1
1 University of New South Wales
Actuarial Studies, Australian School of Business
b.avanzi@unsw.edu.au
Week 6
1/27
Financial Mathematics: Week 6
Plan
Fixed Rate Securities
Denitions and n

Financial Mathematics: Week 2
Week 2
Real vs money rates of interest
Force of interest
Nominal vs eective rate of interest
Comparing sets of cash ows
Discount interest
Plan
Benjamin Avanzi1
Financial Mathematics
1 University of New South Wales
Actuarial S

Financial Mathematics: Week 1
Week 1
Comparing sets of cash ows
Dierent forms of accumulation
Translate a situation into a mathematical model
The time value of money
Course administration
Plan
Benjamin Avanzi1
Financial Mathematics
1 University of New Sou

Financial Mathematics: Week 5
Financial Mathematics: Week 5
Plan
Financial Mathematics
Loans and Repayment Schedule
Recursive approach
Loan Schedule
Benjamin Avanzi1
1 University of New South Wales
Actuarial Studies, Australian School of Business
b.avanzi

Financial Mathematics: Week 6
Financial Mathematics: Week 6
Plan
Fixed Rate Securities
Denitions and notation
Pricing
Makeham Formula
Other relevant elements for calculating the price
Financial Mathematics
Benjamin Avanzi1
Yield and reinvestment rates
Den

ACTL2002
Probability Distributions used in Insurance & Finance
Probability Distributions
used in
Insurance and Finance
S12009
1
ACTL2002
Probability Distributions used in Insurance & Finance
1
Bernoulli Distribution
Discrete distribution
The outcome in a