Lecture Presentation Software
to accompany
Investment Analysis and
Portfolio Management
Eighth Edition
by
Frank K. Reilly & Keith C. Brown
Chapter 22
Chapter 22
Option Contracts
Questions to be answered:
• How are options traded on exchanges and in OTC
markets?
• How are options for stock, stock indexes, foreign
currency, and futures contracts quoted in the
financial press?
• How can investors use option contracts to hedge
an existing risk exposure?
Chapter 22
Option Contracts
• What are the three steps in establishing the
fundamental “no arbitrage” value of an option
contract?
• What is the binomial (or two-state) option pricing
model and in what ways is it an extension of the
basic valuation approach?
• What is the Black-Scholes option pricing model
and how does it extend the binomial valuation
approach?
Chapter 22
Option Contracts
• What is the relationship between the BlackScholes and the put-call parity valuation models?
• How does the payment of a dividend by the
underlying asset impact the value of an option?
• How can models for valuing stock options be
adapted to other underlying assets, such as stock
indexes, foreign currency, or futures contracts?
Chapter 22
Option Contracts
• How do American- and European-style options
differ from one another?
• What is implied volatility and what is its role in
the contract valuation process?
Chapter 22
Option Contracts
• How do investors use options with the underlying
security or in combination with one another to
create payoff structures tailored to a particular
need or view of future market conditions?
• What differentiates a spread from a straddle, a
strangle, or a range forward?
Derivatives
• Forwards
– fix the price or rate of an underlying asset
• Options
– allow holders to decide at a later date whether
such fixing is in their best interest
Option Market Conventions
• Option contracts have been traded for centuries
• Customized options traded on OTC market
• In April 1973, standardized options began
trading on the Chicago Board Option Exchange
• Options Clearing Corporation (OCC) acts as
guarantor of each CBOE -traded options
Price Quotations for
Exchange-Traded Options
• Equity options
–
–
–
–
CBOE, AMEX, PHLX, PSE
typical contract for 100 shares
require secondary transaction if exercised
time premium affects pricing
Price Quotations for
Exchange-Traded Options
• Stock index options
– only settle in cash
• Foreign currency options
– allow sale or purchase of a set amount of non-USD
currency at a fixed exchange rate
– quotes in USD
• Options on futures contracts
– Give the right, but not the obligation, to enter into a
futures contract on an underlying security or
commodity at a later date at a predetermined price
The Fundamentals of Option Valuation
• Risk reduction tools when used as a hedge
• Forecasting the volatility of future asset prices
– direction and magnitude
• Hedge ratio is based on the range of possible
option outcomes related to the range of possible
stock outcomes
• Risk-free hedge buys one share of stock and
sells call options to neutralize risk
• Hedge portfolio should grow at the risk-free rate
The Binomial Option Pricing Model
• Two-state option pricing model
– up movement or down movement
– forecast stock price changes from one subperiod to
the next
• up change
• down change
• number of subperiods
Cj 
rd
p
ud
 p C ju  1  p C jd
r
The Binomial Option Pricing Model
N
 n
N!
N j
j
j N j
Co  
p 1  p  max 0, u d
S  X r
 j 0  N  j ! j!

 


N
 n
N!
N j
j
j N j
Co  
p 1  p 
u d
S  X r
 j m N  j ! j!


hj 
u  d S j
C
jd
 C ju 


The Black-Scholes Valuation Model
• Continuous changes rather than discrete
• Geometric Brownian motion
– volatility factor, s

N d 
 ln S X   RFR  0.5s T   s T  
C 0  SN d1   X e
d1
S
12
  T   s T 
S
  RFR T
2
2
d 2  d1  s T 
12
12
The Black-Scholes Valuation Model
1.
2.
3.
4.
5.
Value is a function of five variables:
Current security price
Exercise price
Time to expiration
Risk-free rate
Security price volatility
C = f(S, X, T, RFR, s)
Estimating Volatility
• Mean and standard deviation of a series of price
relatives
N
1
 
R    Rt
 N  t 1
2
 1 
s 
 Rt  R 
 N  1  t 1
N
2
Problems With
Black-Scholes Valuation
• Stock prices do not change continuously
• Arbitrageable differences between option values
and prices (due to brokerage fees, bid-ask
spreads, and inflexible position sizes)
• Risk-free rate and volatility levels do not remain
constant until the expiration date
Problems With
Black-Scholes Valuation
• Empirical studies showed that the BlackScholes model overvalued out-of-themoney call options and undervalued in-themoney contracts
• Any violation of the assumptions upon
which the Black-Scholes model is based
could lead to a misevaluation of the option
contract
Option Valuation:
Extensions and Advanced Topics
• Valuing European-style put options
• Valuing options on dividend-bearing
securities
• Valuing American-style options
• Stock index options
• Foreign currency options
• Futures options
Option Trading Strategies
• Options are a leveraged alternative to
making a direct investment in the asset on
which the contract is based
• Put options could be used in conjunction
with an existing portfolio to limit the
portfolio’s loss potential
Option Trading Strategies
•
•
•
•
•
•
•
Protective put options
Covered call options
Straddles, strips, and straps
Strangle
Chooser options
Spreads
Range forwards
The Internet
Investments Online
http://www.cboe.com/
http://www.optionmax.com
http://www.finance.wat.ch/cbt/options
http://www.coveredcall.com
End of Chapter 22
–Option Contracts
Future topics
Chapter 23
• Swap Contracts, Convertible Securities, and
Other Embedded Derivatives