ACTL3004/5109 FINANCIAL ECONOMICS
Model Solutions to Tutorial 10
1. Recall that the value of a European put option according to the Black-Scholes is
r (T t)
Vt = Ke
where
log
d1 =
and d2 = d1 +
p
T
K
St
(d2 )
r+1
2
p
Tt
St (d1 )
2
(T
t)
t:
(a) Using the g
ACTL3004/5109 FINANCIAL ECONOMICS
Model Solutions to Tutorial 9
1. In a Brownian motion framework, one can either specify the stock price as a function
of a Brownian motion eg
12
S (t) = S (0) e( 2 )t+W (t)
or alternatively one can specify its dynamics vi
ACTL3004/5109 FINANCIAL ECONOMICS
Tutorial 10 Questions
1. You are given the following information about a European put option on a non-dividend
paying stock:
current stock price:
S
risk-free rate, compounded continuously: 5%
volatility parameter:
0:2
put
ACTL3004/5109 FINANCIAL ECONOMICS
Tutorial 9 Questions
1. Discuss two methods that can be used to build a continuous time nancial model, say,
for a stock price.
2. Derive Ito lemma using the Taylor series argument.
s
(a) For some X (t) = F (W (t) where F
ACTL3004: Week 10a
Financial Economics for Insurance and
Superannuation: Week 10a
Black Scholes Option Pricing Model
1 / 16
ACTL3004: Week 10a
Black-Scholes Model
Derivation
Black-Scholes Model Derivation
The price of a derivative in the Black Scholes mod
ACTL3004/5109 FINANCIAL ECONOMICS
Lecture 10 - Additional Exercise
Consider an executive from a listed company C-Corporation. As a general rule, executives
are awarded company stocks to encourage them to deliver performance for their shareholders.
Executi
ACTL3004: Weeks 9-10
Financial Economics for Insurance and
Superannuation: Week 9-10
Continuous Time Derivative Valuation
1 / 43
ACTL3004: Weeks 9-10
Measure Theory
Radon-Nikodym Derivative
Change of Measure
Eg. Consider the two step random walk tree.
Wit
ACTL3004: Weeks 9-10
Financial Economics for Insurance and
Superannuation: Week 9-10
Continuous Time Derivative Valuation
1 / 43
ACTL3004: Weeks 9-10
Measure Theory
Radon-Nikodym Derivative
Change of Measure
Eg. Consider the two step random walk tree.
Wit
ACTL3004/5109 FINANCIAL ECONOMICS
Model Solutions to Tutorial 6
1.
(a) A
European option allows the holder to exercise the option only at the expiry
of the option. In contrast, an
Americanoption allows the holder to exercise the
option at any time durin
ACTL3004/5109 FINANCIAL ECONOMICS
Tutorial 6 Questions
1. (a) Explain the dierence between a
Europeanand an
Americanoption.
(b) Give reasons why an individual might wish to purchase a call option.
2. .
(a) Explain what is meant by the
intrinsic valueof
ACTL3004: Week 6
Financial Economics for Insurance and
Superannuation: Week 6
Introduction to Derivatives
1 / 21
ACTL3004: Week 6
Derivatives
What is a Derivative Instrument?
What is a Derivative Instrument?
A derivative is a security/contract that promis
ACTL3004: Week 6
Financial Economics for Insurance and
Superannuation: Week 6
Introduction to Derivatives
1 / 21
ACTL3004: Week 6
Derivatives
What is a Derivative Instrument?
What is a Derivative Instrument?
A derivative is a security/contract that promis
ACTL3004/5109 FINANCIAL ECONOMICS
Tutorial 5 Questions
1. Explain what is meant by diversiable and non-diversiable risks of a security. Explain
how the expected return depend on each of these two types of risk under the Single
index model.
2. Expalin what
ACTL3004/5109 FINANCIAL ECONOMICS
Model Solutions to Tutorial 5
1. Under the Single-Index model, there are two distinct risks of a security, where risk
is dened to be the standard deviation of returns over successive periods of time.
Diversiable (or speci
ACTL3004/5109 FINANCIAL ECONOMICS
Tutorial 4 Questions
1. A security analyst forecasts that each of three scenarios for the next year is equally
likely: (1) a boom, (2) controlled growth, and (3) a severe recession. Under these
three states of the world,
ACTL3004/5109 FINANCIAL ECONOMICS
Model Solutions to Tutorial 4
1. First, we nd the means and variances of security A and the market. For security A,
its mean is
1
E (RA ) = (0.25 + 0.20 0.10) = 0.1167
3
and variance is
1
V ar (RA ) = 0.252 + 0.202 + 0.10
ACTL3004: Weeks 4-5
Financial Economics for Insurance and
Superannuation: Weeks 4-5
The Capital Asset Pricing Model and Factor Models
1/1
ACTL3004: Weeks 4-5
Capital Asset Pricing Model
Assumptions
Assumptions: Individuals
1. Investors have the same one-p
ACTL3004/5109 FINANCIAL ECONOMICS
Tutorial 2 Questions
1. On measures of investment risk :
(a) Dene the following measures of investment risk:
i. variance of return;
ii. downside semi-variance of return; and
iii. shortfall probability.
(b) Give advantages
ACTL3004/5109 FINANCIAL ECONOMICS
Model Solutions to Tutorial 2
1. (a) Dene the following measures of investment risk:
i. variance of return; (r )2 f (r) dr where is the mean return and f (r)
is the p.d.f. of return.
ii. downside semi-variance of return;
ACTL3004/5109 FINANCIAL ECONOMICS
Model Solutions to Tutorial 1
1. Luenberger, Chapter 9. Questions 1,2,5,6.
(a) The possible outcomes and utility are:
Income 80
90 100 110 120 130 140
U tility 2.99 3.08 3.16 3.23 3.31 3.38 3.44
The total utility is the a
ACTL3004/5109 FINANCIAL ECONOMICS
Tutorial 1 Questions
1. Luenberger, Chapter 9. Questions 1,2,5,6.
2. Explain the expected utility theorem and explain the four axioms that are required to
derive the expected utility theorem.
3. An investment oers a rate
Week 1: Utility Theory, Preferences Representation
Often given distribution of return (or loss) f (x)
with wealth k (x) eg w = a + bx
But expected Z
utility theory requires
up
u (w) g (w) dw
low
with g the density of w. What do we do?
From prob theory, if
11.1 Learning Outcomes
The aim of this assignment is to develop your skills in the following :
Understanding the basics of stochastic calculus in the context of modelling returns of a
market quantity used to price a financial product.
Explaining the conce
ACTL3004/5109 Financial Economics for Superannuation and Insurance
2010 Assignment Citigroup MLI Case Study
Model Solutions
Section 1 Introduction and Mathematical Derivation
a.) The MLI Growth Kicker is a structured investment product with the following
ECON1203/ECON2292
Business and Economic
Statistics
Week 12
Week 12 topics
l Regression
case study
l Chi-squared distribution
l
l
l
Hypothesis test for a population variance
Chi-squared test of goodness of fit
Chi-squared test of a contingency table
l Key
ECON1203/ECON2292
Business and Economic
Statistics
Week 11
Week 11 topics
l Prediction
in linear regression
l Multiple regression model
l
Interpretation & inference
l Key
l
references
Keller 16.5, 17.1-2
2
Prediction in regression
l
l
One of the main uses
ECON1203/ECON2292
Business and Economic
Statistics
Week 10
Week 10 topics
l Simple
l
l
l
Method of least squares
Basic assumptions of regression model
Inference & explanatory power
l Key
l
linear regression
references
Keller Chapter 16 and 13.1
2
Recall (
ECON1203/ECON2292
Business and Economic
Statistics
Week 9
Week 9 topics
l
Calculating probability of type 2 errors
l
l
Hypothesis testing & confidence intervals for the
mean when population variance is unknown
l
l
t distribution
Sampling distribution of s