Transcript Document

Chapter 15 (4th)
Chapter 17 (5th)
Principles of
Options and Option Pricing
Portfolio Construction, Management, & Protection, 4e, Robert A. Strong
Copyright ©2006 by South-Western, a division of Thomson Business & Economics. All rights reserved.
1
Introduction
 Innovations
in stock options have been
among the most important developments in
finance in the last 20 years
 The cornerstone of option pricing is the
Black-Scholes Option Pricing Model
(OPM)
2
Option Principles
 Why
Options Are a Good Idea
 What Options Are
 Standardized Option Characteristics
 Where Options Come From
 Where and How Options Trade
 The Option Premium
 Sources of Profits and Losses with Options
3
Why Options Are a Good Idea
 Options:
• Give the marketplace opportunities to adjust
risk or alter income streams that would
otherwise be unavailable
• Provide financial leverage
• Can be used to generate additional income from
investment portfolios
4
Why Options Are
a Good Idea (cont’d)
 The
investment process is dynamic:
• The portfolio manager needs to constantly
reassess and adjust portfolios with the arrival of
new information
 Options
are more convenient and less
expensive than wholesale purchases or sales
of stock
5
What Options Are:
Call Options
 A call
option gives you the right to buy
within a specified time period at a specified
price
 The
owner of the option pays a cash
premium to the option seller in exchange
for the right to buy
6
Put Options
 A put
option gives you the right to sell
within a specified time period at a specified
price
 It
is not necessary to own the asset before
acquiring the right to sell it
7
Standardized
Option Characteristics
 All
exchange-traded options have
standardized expiration dates
• The Saturday following the third Friday of
designated months for most options
• Investors typically view the third Friday of the
month as the expiration date
8
Standardized
Option Characteristics (cont’d)
 The
striking price of an option is the
predetermined transaction price
• In multiples of $2.50 (for stocks priced $25.00
or below) or $5.00 (for stocks priced higher
than $25.00)
• There is usually at least one striking price
above and one below the current stock price
9
Standardized
Option Characteristics (cont’d)
 Puts
and calls are based on 100 shares of the
underlying security
• The underlying security is the security that the
option gives you the right to buy or sell
• It is not possible to buy or sell odd lots of
options
10
Where Options Come From:
Introduction
 If
you buy an option, someone has to sell it
to you
 No
set number of put or call options exists
• The number of options in existence changes
every day
• Option can be created and destroyed
11
Opening and
Closing Transactions
 The
first trade someone makes in a
particular option is an opening transaction
• An opening transaction that is the sale of an
option is called writing an option
12
Opening and
Closing Transactions (cont’d)
 The
trade that terminates a position by
closing it out is a closing transaction
• Options have fungibility
– Market participants can reverse their positions by
making offsetting trades
– e.g., the writer of an option can close out the
position by buying a similar one
13
Opening and
Closing Transactions (cont’d)
 The
owner of an option will ultimately:
• Sell it to someone else
• Let it expire or
• Exercise it
14
Role of the
Options Clearing Corporation
 The
Options Clearing Corporation (OCC):
• Positions itself between every buyer and seller
• Acts as a guarantor of all option trades
• Regulates the trading activity of members of
the various options exchanges
• Sets minimum capital requirements
• Provides for the efficient transfer of funds
among members as gains or losses occur
15
OCC-Related
Information on the Web
16
Where and How Options Trade

In the United States, options trade on five
principal exchanges:
• Chicago Board Options Exchange (CBOE)
• American Stock Exchange (AMEX)
• Philadelphia Stock Exchange
• Pacific Stock Exchange
• International Securities Exchange
17
Where and How
Options Trade (cont’d)
 AMEX
and Philadelphia Stock Exchange
options trade via the specialist system
• All orders to buy or sell a particular security
pass through a single individual (the specialist)
• The specialist:
– Keeps an order book with standing orders from
investors and maintains the market in a fair and
orderly fashion
– Executes trades close to the current market price if
no buyer or seller is available
18
Where and How
Options Trade (cont’d)
 CBOE
and Pacific Stock Exchange options
trade via the marketmaker system
• Competing marketmakers trade in a specific
location on the exchange floor near the order
book official
• Marketmakers compete against one another for
the public’s business
19
Where and How
Options Trade (cont’d)
 Any
given option has two prices at any
given time:
• The bid price is the highest price anyone is
willing to pay for a particular option
• The asked price is the lowest price at which
anyone is willing to sell a particular option
20
The Option Premium:
Intrinsic Value and Time Value
 The
price of an option has two components:
• Intrinsic value:
– For a call option equals the stock price minus the
striking price
– For a put option equals the striking price minus the
stock price
• Time value equals the option premium minus
the intrinsic value
21
Intrinsic Value and
Time Value (cont’d)
 An
option with no intrinsic value is out of
the money
 An
option with intrinsic value is in the
money
 If
an option’s striking price equals the stock
price, the option is at the money
22
The Financial Page Listing
 The
following slide shows an example from
the online edition of The Wall Street
Journal:
• The current price for a share of Disney stock is
$21.95
• Striking prices from $20 to $25 are available
• The expiration month is in the second column
• The option premiums are provided in the “Last”
column
23
The Financial Page Listing
24
The Financial
Page Listing (cont’d)
 Investors
identify an option by company,
expiration, striking price, and type of
option:
Disney JUN 22.50 Call
Company
Expiration
Striking
Price
Type
25
The Financial
Page Listing (cont’d)

The Disney JUN 22.50 Call is out of the money
• The striking price is greater than the stock price
• The time value is $0.25

The Disney JUN 22.50 Put is in the money
• The striking price is greater than the stock price
• The intrinsic value is $22.50 - $21.95 = $0.55
• The time value is $1.05 - $0.55 = $0.50
26
HW 1. Smith electronics (SELE), price $ $66.38
Striking Price
Calls
Puts
Jan. Feb. April
Jan. Feb. April
60
6.38 8.25 9
0.06 0.75 0.88
65
2.50 4.88 6.75
0.69 2.25 3.50
75
0.06 1.13 2.50
8.38 9
9.75

A. How much time value is in a SELE Feb 60 call option?
Answer: premium- intr. value = 8.25 – (66.38 - 60) = 1.87
B. What is the intrinsic value of a SELE Jan 65 call?
Answer: Intr. Value = price – str. price = 66.38 – 65 = 1.38
C. What is the intrinsic value of a SELE APR 75 put?
Answer: str. price – price = 75 – 66.38 = 8.62
27
The Financial
Page Listing (cont’d)
 As
an option moves closer to expiration, its
time value decreases
• Time value decay
 An
option is a wasting asset
• Everything else being equal, the value of an
option declines over time
28
Sources of Profits and
Losses with Options:
Option Exercise
 An
American option can be exercised at
any time prior to option expiration
• It is typically not advantageous to exercise
prior to expiration since this amount to
foregoing time value
 European
options can be exercised only at
expiration
29
Exercise Procedures
 The
owner of an option who decides to
exercise the option:
• Calls her broker
• Must put up the full contract amount for the
option
– The premium is not a down payment on the option
terms
30
Exercise Procedures (cont’d)
 The
option writer:
• Must be prepared to sell the necessary shares to
the call option owner
• Must be prepared to buy shares of stock from
the put option owner
31
Exercise Procedures (cont’d)
 In
general, you should not buy an option
with the intent of exercising it:
• Requires two commissions
• Selling the option captures the full value
contained in an option
32
Profit and Loss Diagrams
 For
the Disney JUN 22.50 Call buyer:
Breakeven Point = $22.75
Maximum profit
is unlimited
$0
-$0.25
Maximum loss
$22.50
33
Profit and Loss Diagrams
(cont’d)
 For
the Disney JUN 22.50 Call writer:
Maximum profit
Breakeven Point = $22.75
$0.25
$0
Maximum loss
is unlimited
$22.50
34
Profit and Loss Diagrams
(cont’d)
 For
the Disney JUN 22.50 Put buyer:
Maximum profit = $21.45
Breakeven Point = $21.45
$0
-$1.05
Maximum loss
$22.50
35
Profit and Loss Diagrams
(cont’d)
 For
the Disney JUN 22.50 Put writer:
Maximum profit
Breakeven Point = $21.45
$1.05
$0
Maximum loss = $21.45
$22.50
36
 HW
2. Suppose you simultaneously buy
400 shares of SELE (for price $66.38)and
write two FEB 70 puts (for a premium of
$5). What is your gain or loss if, at option
expiration, the common stock of SELE sells
for $57.38?
Answer: gain/loss on stock + gain/loss on
option + premium
= 400 (57.38-66.38) + 200 (57.38-70) +
200(5) = -3,600- 2,524 + 1,000=-$5, 124
37
 HW
3. In problem 2, what is your profit or
loss if SELE stock is $77.38 at option
expiration?
Answer: You have a gain on the stock and the
puts expire worthless:
400 x (77.38 – 66.38) + 200 (5) = $5,400
38
Option Pricing
Determinants of the Option Premium
 Black-Scholes Option Pricing Model
 Development and Assumptions of the Model
 Insights into the Black-Scholes Model
 Delta
 Theory of Put/Call Parity
 Stock Index Options

39
Determinants of the
Option Premium:
Market Factors
 Striking
price
• For a call option, the lower the striking price,
the higher the option premium
 Time
to expiration
• For both calls and puts, the longer the time to
expiration, the higher the option premium
40
Market Factors (cont’d)
 Current
stock price
• The higher the stock price, the higher the call
option premium and the lower the put option
premium
 Volatility
of the underlying stock
• The greater the volatility, the higher the call and
put option premium
41
Market Factors (cont’d)

Dividend yield on the underlying stock
• Companies with high dividend yields have a smaller
call option premium than companies with low dividend
yields
[Subtract the present value of the dividend from the stock price in the
OPM]

Risk-free interest rate
• The higher the risk-free rate, the higher the call option
premium
42
Accounting Factors
 Stock
splits:
• The OCC will make the following adjustments:
– The striking price is reduced by the split ratio
– The number of options is increased by the split ratio
43
Black-Scholes
Option Pricing Model

The Black-Scholes OPM:
C  S N (d1 )  Ke  Rt N (d 2 )


ln(S / K )  R  ( / 2) t
d1 
 t
2
d 2  d1   t
44
Black-Scholes
Option Pricing Model (cont’d)
 Variable
•
•
•
•
•
definitions:
C = theoretical call premium
S = current stock price
t = time in years until option expiration
K = option striking price
R = risk-free interest rate
45
Black-Scholes
Option Pricing Model (cont’d)
 Variable
definitions (cont’d):
•  = standard deviation of stock returns
• N(x) = probability that a value less than “x” will
occur in a standard normal distribution
• ln = natural logarithm
• e = base of natural logarithm (2.7183)
46
Black-Scholes
Option Pricing Model (cont’d)
Example
Stock ABC currently trades for $30. A call option on ABC
stock has a striking price of $25 and expires in three
months. The current risk-free rate is 5%, and ABC stock
has a standard deviation of 0.45.
According to the Black-Scholes OPM, what should be the
premium for this option?
47
Black-Scholes
Option Pricing Model (cont’d)
Example (cont’d)
Solution: We must first determine d1 and d2:
d1 

ln( S / K )   R  ( 2 / 2)  t
 t
ln(30 / 25)  0.05  (0.452 / 2)  0.25
0.45 0.25
0.1823  0.0378

 0.978
0.225
48
Black-Scholes
Option Pricing Model (cont’d)
Example (cont’d)
Solution (cont’d):
d 2  d1   t
 0.978  (0.45) 0.25
 0.978  0.225
 0.753
49
Black-Scholes
Option Pricing Model (cont’d)
Example (cont’d)
Solution (cont’d): The next step is to find the normal
probability values for d1 and d2. Using Microsoft Excel’s
NORMSDIST function yields:
N (d1 )  0.836
N (d2 )  0.774
50
Black-Scholes
Option Pricing Model (cont’d)
Example (cont’d)
Solution (cont’d): The final step is to calculate the option premium:
C  S N (d1 )  Ke  Rt N (d 2 )
 $300.836  $25( 0.05)( 0.25) 0.774
 $25.08  $19.11
 $5.97
51
Using Microsoft Excel’s
NORMSDIST Function
 The
Excel portion below shows the input
and the result of the function:
52
Development and
Assumptions of the Model
Introduction
 The Stock Pays No Dividends during the Option’s
Life
 European Exercise Terms
 Markets are Efficient
 No Commissions
 Constant Interest Rates
 Lognormal Returns

53
Introduction
 Many
of the steps used in building the
Black-Scholes OPM come from:
• Physics
• Mathematical shortcuts
• Arbitrage arguments
 The
actual development of the OPM is
complicated
54
The Stock Pays No Dividends during
the Option’s Life
 The
OPM assumes that the underlying
security pays no dividends
 The OPM can be adjusted for dividends:
• Discount the future dividend assuming
continuous compounding
• Subtract the present value of the dividend from
the stock price in the OPM
• Compute the premium using the OPM with the
adjusted stock price
55
European Exercise Terms
 The
OPM assumes that the option is
European
 Not
a major consideration since very few
calls are ever exercised prior to expiration
56
Markets are Efficient
 The
OPM assumes markets are
informationally efficient
• People cannot predict the direction of the
market or of an individual stock
57
No Commissions
 The
OPM assumes market participants do
not have to pay any commissions to buy or
sell
 Commissions paid by individual investors
can significantly affect the true cost of an
option
• Trading fee differentials cause slightly different
effective option prices for different market
participants
58
Constant Interest Rates
 The
OPM assumes that the interest rate R in
the model is known and constant
 It
is common use to use the discount rate on
a U.S. Treasury bill that has a maturity
approximately equal to the remaining life of
the option
• This interest rate can change
59
Lognormal Returns
 The
OPM assumes that the logarithms of
returns of the underlying security are
normally distributed
 A reasonable
assumption for most assets on
which options are available
60
Insights into the
Black-Scholes Model

Divide the OPM into two parts:
C  S N (d1 )  Ke
Part A
 Rt
N (d2 )
Part B
61
Insights into the
Black-Scholes Model (cont’d)
 Part A is
the expected benefit from
acquiring the stock:
• S is the current stock price and the discounted
value of the expected stock price at any future
point
• N(d1) is a pseudo-probability
– It is the probability of the option being in the money
at expiration, adjusted for the depth the option is in
the money
62
Insights into the
Black-Scholes Model (cont’d)
 Part
B is the present value of the exercise
price on the expiration day:
• N(d2) is the actual probability the option will be
in the money on expiration day
 The
value of a call option is the difference
between the expected benefit from
acquiring the stock and paying the exercise
price on expiration day
63
Delta
 Delta
is the change in option premium
expected from a small change in the stock
price, all other things being the same:
C

S
C
where
 the first partial derivative of the call premium
S
with respect to the stock price
64
Delta (cont’d)
 Delta
allows us to determine how many
options are needed to mimic the returns of
the underlying stock
 Delta
is exactly equal to N(d1)
• e.g., if N(d1) is 0.836, a $1 change in the price
of the underlying stock price leads to a change
in the option premium of 84 cents
65
Theory of Put/Call Parity
 The
following variables form an interrelated
securities complex:
•
•
•
•
Price of a put
Price of a call
The value of the underlying stock
The riskless rate of interest
66
Theory of
Put/Call Parity (cont’d)
 The
put/call parity relationship:
K
CPS
(1  R )T
where C  price of a call
P  price of a put
K  option striking price
R  risk-free interest rate
T  time until expiration in years
67
Stock Index Options
 Stock
index options are the option
exchanges’ most successful innovation
• e.g., the S&P 100 index option
 Index
options have no delivery mechanism
• All settlements are in cash
68
Stock Index Options (cont’d)
 The
owner of an in-the-money index call
receives the difference between the closing
index level and the striking price
 The
owner of an in-the-money index put
receives the difference between the striking
price and the index level
69