Valuing Stock Options:
The Black-Scholes-Merton
Model
Chapter 13
Fundamentals of Futures and Options Markets, 9th Ed, Ch 13, Copyright John C. Hull 2016
1
The Black-Scholes-Merton
Random Walk Assumption
Consider
a stock whose price is S
In a short perio
Interest Rates
Chapter 4
Fundamentals of Futures and Options Markets, 9th Ed, Ch 4, Copyright John C. Hull 2016
1
Types of Rates
Treasury
rate
LIBOR
Fed
funds rate
Repo rate
Fundamentals of Futures and Options Markets, 9th Ed, Ch 4, Copyright John C.
CHAPTER 12
Introduction to Binomial Trees
Practice Questions
Problem 12.8.
Consider the situation in which stock price movements during the life of a European option
are governed by a two-step binomial tree. Explain why it is not possible to set up a posi
Introduction
Chapter 1
Fundamentals of Futures and Options Markets, 9th Ed, Ch 1, Copyright John C. Hull 2016
1
The Nature of Derivatives
A derivative is an instrument whose value
depends on the values of other more
basic underlying variables
Derivatives
CHAPTER 13
Valuing Stock Options: The Black-Scholes-Merton Model
Practice Questions
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 probability distribution for the
Mechanics of Options
Markets
Chapter 9
Fundamentals of Futures and Options Markets, 9th Ed, Ch 9, Copyright John C. Hull 2016
1
Types of Options
A
call is an option to buy
A put is an option to sell
A European option can be exercised only
at the end of
Trading Strategies
Involving Options
Chapter 11
Fundamentals of Futures and Options Markets, 9th Ed, Ch 11, Copyright John C. Hull 2016
1
Strategies to be Considered
Bond
plus option to create principal
protected note
Stock plus option
Two or more opti
Securitization and the
Credit Crisis of 2007
Chapter 8
Fundamentals of Futures and Options Markets 9th Ed, Ch 8, Copyright John C. Hull 2016
1
Securitization
Traditionally
banks have funded loans with
deposits
Securitization is a way that loans can
incr
CHAPTER 3
Hedging Strategies Using Futures
Practice Questions
Problem 3.8.
In the CME Groups corn futures contract, the following delivery months are available:
March, May, July, September, and December. State the contract that should be used for
hedging
CHAPTER 9
Mechanics of Options Markets
Practice Questions
Problem 9.8.
A corporate treasurer is designing a hedging program involving foreign currency options.
What are the pros and cons of using (a) the NASDAQ OMX and (b) the over-the-counter
market for
CHAPTER 10
Properties of Stock Options
Practice Questions
Problem 10.8.
Explain why the arguments leading to putcall parity for European options cannot be used to
give a similar result for American options.
When early exercise is not possible, we can argu
CHAPTER 2
Futures Markets and Central Counterparties
Practice Questions
Problem 2.8.
The party 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
CHAPTER 6
Interest Rate Futures
Practice Questions
Problem 6.8.
The price of a 90-day Treasury bill is quoted as 10.00. What continuously compounded
return (on an actual/365 basis) does an investor earn on the Treasury bill for the 90-day
period?
The cash
CHAPTER 1
Introduction
Practice Questions
Problem 1.8.
Suppose you own 5,000 shares that are worth $25 each. How can put options be used to
provide you with insurance against a decline in the value of your holding over the next four
months?
You should buy
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
CHAPTER 7
Swaps
Practice Questions
Problem 7.8.
A bank enters into an interest rate swap with a nonfinancial counterparty using bilaterally
clearing where it is paying a fixed rate of 3% and receiving LIBOR. No collateral is
posted and no other transactio
CHAPTER 4
Interest Rates
Practice Questions
Problem 4.8.
The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond
that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that
will pay cou
Chapter 8
Securitization and the Credit Crisis of 2007
Practice Questions
Problem 8.8.
Why did mortgage lenders frequently not check on information provided by potential
borrowers on mortgage application forms during the 2000 to 2007 period?
Subprime mort
Face Value
$
Actual Value
Assets
100,000,000 $
90,000,000
Senior Tranche
80%
Mezzanine Tranche (BBB)
15%
Equity Tramche
5%
Losses on Subprime Losses on Mezzanine Losses on Equity
portfolios
Tranche of ABS
Tranche of ABS
CDO
10%
33.33%
100.00%
Losses on Su
Hedging Oil using roll-over
Amount to hedge
1,000,000 barrels
Position
Short
Current time
Apr-13
Time needed
Jun-14
Hedge Ratio
1
Current Sport Price
$89
Contract size
$1,000 barrels
Policy - maturity of hedging futures should be less than 6 months
Date
S
Portfolio Beta
Portfolio size (in $)
$
Index level
Futures Price
Contract size
1,250
$
Dividend yield
Risk-free rate
1,259.00
250
3% per annum
6% per annum
Number of Contracts
Rounded
138.2049
138
Holding period
Dividend yield over 2 months
Index now
Inde
Mini-homework Chapter 2
Derivatives
Color Coding
Given
Calculations
Final Answer
2.11
2.11
Contract Size
Qty of contracts. Qf
F
Initial Margin
Maintenance Margin
$
$
15,000 Pounds
2
1.600 per pound
6,000
4,500 per contract
Minimum Net loss required for a