Tutorial #11
 Greeks III
 Volatility Smiles
(Chapter 17, 19 of Hulls Textbook, 8th. edition)
Problem 1.
A financial institution has just sold 10,000 European call options on NAB stock. Each option
is written on one share of the underlying stock. The opt
FNCE30007 PRACTICE QUESTIONS FINAL EXAM
QUESTION 1
Consider a European call option on a nondividend paying stock with a strike of $50 and an
expiration date in two years. The stock price is $52 and the risk free rate is 5% p.a. The call is priced
at $5.
Tutorial #8
Implied Volatility
Options on Stock Indices
(from Chapter 13 and 15 of Hulls Textbook, 8th. edition)
1. In class we looked at the relative movements of the VIX and the S&P500 index. Which of
the following statements is true?
a) The VIX tends t






Stochastic process
o Sequence of related rv over time
o i.e. there is physical link between them
o we model movements in stock prices over time by a stochastic process
Riskless hedge
o Key concept underlying most standard option pricing models
FNCE 30007 DERIVATIVE SECURITIES
Tutorial solution
Binomial II
Question 1
Question 2
American put early exercise may be optimal at any time t<T. Need to check all nodes.
Node 4:
Similarly
Node
5
6
2
3
1
Value exercised = 5052.02 = 2.02
Value not exercis
Tutorial #7
Valuing Stock Options: The BlackScholesMerton Model
(from Chapter 13 of Hulls Textbook, 8th. edition)
Problem 13.8
A stock price is currently $40. Assume that the expected return from the stock is
15% and its volatility is 25%. What is the p
Derivative Securities
Tutorial : Properties of Stock Options  Solutions
Question 1
What is the lower bound for the price of a sixmonth call option on a nondividendpaying
stock when the stock price is $80, the strike price is $75, and the riskfree int
FNCE 30007 DERIVATIVE SECURITIES
Tutorial Solutions
The Binomial Model (Part I)
Question 1
i)
ii) The above table shows there are 36 possible outcomes that are equally likely.
P ( X 7) p (7) 6 / 36 1 / 6
iii)
xi
2
3
4
5
6
7
8
9
10
11
12
p ( xi )
1/36
2/36
Tutorial #9
Options on Stock Indices
Currency Options
Delta
(from Chapter 15 and 17 of Hulls Textbook, 8th. edition)
1.
You hold an equity portfolio and want to buy insurance on it using put options. Which of the following is
true?
a) the cost of the insu
Tutorial #8
Implied Volatility
Options on Stock Indices
(from Chapter 13 and 15 of Hulls Textbook, 8th. edition)
1. In class we looked at the relative movements of the VIX and the S&P500 index. Which of
the following statements is true?
a) The VIX tends t
Tutorial #10
The Greeks II:
Delta, Gamma, Theta
(Chapter 17 of Hulls Textbook, 8th. edition)
1. A European call and European put have the same strike price and time to maturity. Which
of the following statements is true?
(a) The gamma of a call is the sam
Intro
Bond Pricing Zero Coupon Bonds Coupon Bonds Same discount rates Comparative Statics Price evolution Yields Conclusions Appendix
Zero and Coupon Bonds
Antonio Gargano
Investments
University of Melbourne
Semester 1, 2015
1 / 63
Intro
Bond Pricing Zero
Managing
Bond
Portfolios
Antonio Gargano
Key Points
Official
Managing Bond Portfolios
Risks Overview
Intro
Risks
Antonio Gargano
Interest Rate
Sensitivity
intro
1 and 2
3 and 4
5
6
Investments
University of Melbourne
Sum up
Duration
Weighted Average
Semes
FNCE 30007
Derivative Securities
Lecture Introduction to Futures
Outline
Definition
Specifications of futures contracts
How to open and close a position
Relationship between futures price and spot price
Margins and markingtomarket
Price and trading info
Tutorial #11
 Greeks III
 Volatility Smiles
(Chapter 17, 19 of Hulls Textbook, 8th. edition)
Problem 1
A financial institution has just sold 10,000 European call options on NAB stock. Each option
is written on one share of the underlying stock. The opti
 Currency Options Ch. 15
 The Greeks I Ch. 17 Readings:
Chapter 15: 15.2, 15.5
Chapter 17: 17.1, 17.2, 17.4
Currency Options
Currency options trade primarily OTC
There also exists exchange based option trading: in
the US FX options trade on NASDAQ OMX
B
Tutorial #10
The Greeks II:
Delta, Gamma, Theta
(Chapter 17 of Hulls Textbook, 8th. edition)
1. A European call and European put have the same strike price and time to maturity. Which
of the following statements is true?
(a) The gamma of a call is the sam
Tutorial #7
Valuing Stock Options: The BlackScholesMerton Model
(from Chapter 13 of Hulls Textbook, 8th. edition)
Problem 13.8
A stock price is currently $40. Assume that the expected return from the stock is
15% and its volatility is 25%. What is the p
FNCE 30007
Derivative Securities
Lecture Hedging with Futures
Outline
Short/Long Hedges
Should companies hedge?
Basis Risk
Cross Hedging
Use of Stock Index Futures
Hedge Ratio
Reading: Chapter 3
Short and Long Hedges
Objective: take a futures position tha
FNCE 30007
Derivative Securities
Lecture Binomial Model (Part 2)
Outline
The n period model
When early exercise may be optimal
Hedging strategies
Risk neutral valuation
The n period model
Assumptions
1) to 6) as before
T
9) n periods (of equal length) to
Readings:
Chapter 13: 13.1 13.9
Option Valuation: Black, Scholes
and Merton (BSM) Model
(CH 13)
A BIG DEAL
Black and Scholes (1973) and Merton
(1973) won the Nobel Prize in Economics
for their work on option pricing
To this day, the BlackScholes
model/fo
Readings:
Chapter 13: 13.10
Dividends
in Options
Valuation
Chapter 15:
15.1, 15.3,
15.4
1. Including
2. Options on Stock Indices:
 Basic Features
 Portfolio Insurance
Volatility and VIX
VIX and S&P500 tend to move in
opposite directions (negative
correl
 The Greeks II Ch. 17
Readings:
Chapter 17: 17.4 17.6, 17.817.10
Gamma Addresses Delta Hedging
Errors Caused By Curvature
Call
price
C
C
C
Stock price
S
S
Gamma ()
Definition: change in the (portfolios) delta due
to a small change in the underlying asse
FNCE 30007
Derivative Securities
Lecture Forward & futures pricing
Outline
Introduction
Investment assets
Arbitrage
Investment v consumption assets
Short selling
Simple relation (no income)
Known income (bond futures)
Known yield (stock index futures, cur
FNCE 30007 Derivative Securities
Tutorial Questions
The Binomial Model (Part II)
QUESTION 1
Consider a 9 month European call option on a non dividend paying stock. The
underlying stock price is $25, the strike price is $23, the riskfree rate of interest
i
(More) Binomial Trees Ch. 18
Volatility and Smiles Ch. 19
Readings:
Chapter 18: Lecture Notes (no textbook)
Chapter 19:19.119.3
Main Points of Ch. 18
The binomial tree method is flexible enough to
be used for European as well as American
options
B.T. met
FNCE 30007 DERIVATIVE SECURITIES
Tutorial Questions
The Binomial Model (Part I)
QUESTION 1
Assume you roll a pair of fair dice. Let X be the random variable whose value
represents the sum of numbers rolled. Let Y be the random variable whose
value represe
Tutorial #9
Options on Stock Indices
Currency Options
Greeks I: Delta
(from Chapter 15 and 17 of Hulls Textbook, 8th. edition)
1.
You hold an equity portfolio and want to buy insurance on it using put options. Which of the following is
true?
a) the cost o
Overview
Toy Model
Why credit risk?
Credit Risk
Antonio Gargano
Investments
University of Melbourne
Semester 1, 2015
Credit Ratings
Overview
Toy Model
Why credit risk?
Credit Ratings
Seminar Overview
What is credit risk?
How do we quantify it?
Why is i
Performance Evaluation
Miley He
Please note the following questions are only prepared for practice purposes and are NOT
indications for the exam questions.
Question 1:
Jensens alpha measures:
A)
B)
C)
D)
E)
return per
FNCE 30001 Investments
Semester 2, 2017
31 July and 4 August 2017
Week 2: Optimal Portfolio Choice
Emeritus Professor Rob Brown
FNCE 30001 Investments: 2.0
Week 2: Optimal Portfolio Choice
Overview of Lecture
This lecture will cover:
o The Portfolio Const
CHAPTER 5
Determination of Forward and Futures Prices
Practice Questions
Problem 5.8.
Is the futures price of a stock index greater than or less than the expected future value of the
index? Explain your answer.
The futures price of a stock index is always