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
Tutorial 1 Solutions
Futures
Question 1
These options make the contract less attractive to the long position and more attractive to the
short position. This tends to reduce the futures price.
Question 2
A margin is a sum of money deposited by an investor/
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
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
(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 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
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
 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
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
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
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
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
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
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
 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 #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
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
FNCE 30007 DERIVATIVE SECURITIES
Tutorial Questions
Tutorial 1: Futures
Question 1
The part with a short position in a futures contract sometimes has options as to the
precise asset that will be delivered, where delivery will take place, when delivery wil
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.
Practice Questions
QUESTION 1
Consider a European call option on a nondividend paying stock when the stock price is
$25.00, the strike price is $28.00, the riskfree interest rate is 8% per annum, the volatility is
30% per annum and there is four years t
lOMoARcPSD
Sample/practice exam June 2015, questions
Derivative Securities (University of Melbourne)
Distributing prohibited  Downloaded by Ka Man Carrie Chan (carriechinahongkong@hotmail.com)
lOMoARcPSD
Derivative Securities
Seat No:
Student No:
(Do NOT
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 #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 #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
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
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
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
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






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