15
Stock Options
1
Option Basics
• Stock option = derivative security
• Value “derived” from the value of the
underlying common stock (underlying
asset)
• Exchange-traded Option Contracts
• Standardized
• Facilitates trading and price reporting.
• Contract = 100 shares of stock
• Zero-sum game
15-2
2
Put and Call Options
• Call option
• Gives holder the right but not the obligation
to buy the underlying asset at a specified
price at a specified time.
• Put option
• Gives the holder the right but not the
obligation to sell the underlying asset at a
specified price at a specified time.
15-3
3
Options on Common Stock
1.
2.
3.
4.
5.
•
Identity of the underlying stock
Strike or Exercise price
Contract size
Expiration date or maturity
Exercise cycle
American or European
6. Delivery or settlement procedure
15-4
4
Listed
Option
Quotations
www.wsj.com
15-5
Option Price Quotes
• Option Chain:
• List of available option contracts and prices
for a particular security
• Stock option ticker symbols include:
• Letters identify underlying stock
• Letter identifies expiration month & call/put
• A through L for calls; M through X for puts
• Letter identifies strike price
15-6
6
Stock Option Ticker Symbol and Strike
Price Codes
15-7
7
Listed Option Quotes on the Web
15-8
8
Option Naming Convention Changes
• Instituted by the Options Clearing
Corporation
• Length increased from 5 to 21 characters
• New style includes letters and numbers
• Old style presented difficulties:
• Hard to use for Nasdaq stocks
• Hard for investors to interpret
• Proliferation of new option types
15-9
“Old Style” Option Naming Convention
• “OPRA” = Options Price Reporting
Authority
• 5 characters
• Letters only
• 3 data elements
AAQED
1
Root Symbol
2
Expiration-C-P Ind
3
Strike Price
AAQ
E
D
AAQED = call on Apple that expires in May with a $20 strike price
15-10
“New Style” Option Naming Convention
•
•
•
•
“OCC Series Key”
21 characters
Letters and numbers
4 data elements
Old
AAQED
AAPL 100522C00020000
1
New
Root
Symbol
AAPL
2
Exp
Year
10
3
4
Strike
Exp
Exp Day Call/Put
Month
Price $
05
22
C
Strike
Price
dec
00020 000
15-11
Option Price Quotes
Calls
MSFT (MICROSOFT CORP)
$ 25.98
July 2008 CALLS
Strike
Last Sale
Bid
Ask
Vol
Open Int
15.00
10.85
10.95
11.10
10
85
17.50
10.54
8.45
8.55
0
33
20.00
6.00
6.00
6.05
4
729
22.50
3.60
3.55
3.65
195
3891
24.00
2.30
2.24
2.27
422
2464
25.00
1.50
1.45
1.48
3190
10472
26.00
0.83
0.83
0.85
2531
15764
27.50
0.31
0.29
0.31
2554
61529
15-12
12
Option Price Quotes
Puts
MSFT (MICROSOFT CORP)
$ 25.98
July 2008 PUTS
Strike
Last Sale
Bid
Ask
Vol
Open Int
15.00
0.01
0.00
0.01
0
2751
17.50
0.01
0.00
0.02
0
2751
20.00
0.01
0.01
0.02
0
5013
22.50
0.03
0.03
0.04
13
4788
24.00
0.11
0.11
0.12
50
25041
25.00
0.25
0.24
0.25
399
7354
26.00
0.45
0.45
0.47
10212
51464
27.50
0.80
0.82
0.84
2299
39324
15-13
13
Option Price Quotes
MSFT (MICROSOFT CORP)
STRIKE = $25.00
CALLS
Last Sale
July 2008
1.42
August 2008
1.80
October 2008
2.36
January 2009
3.10
Bid
1.45
1.85
2.43
3.15
Ask
1.48
1.87
2.46
3.20
Vol
355
257
41
454
Open Int
10472
927
3309
59244
PUTS
July 2008
August 2008
October 2008
January 2009
Bid
0.45
0.80
1.39
2.06
Ask
0.47
0.82
1.41
2.08
Vol
419
401
215
2524
Open Int
51464
1591
25323
155877
Last Sale
0.47
0.81
1.43
2.09
25.98
15-14
14
The Options Clearing Corporation
•
•
•
•
Private agency
Guarantees contract fulfillment
“Buyer to every seller; seller to every buyer”
Issues and clears all option contracts trading
on U.S. exchanges
• Subject to regulation by the Securities and
Exchange Commission (SEC)
Visit the OCC at: www.optionsclearing.com.
15-15
15
Buying an Option
• Option holder = buyer of an option
contract
• Call option holder has the right but not the
obligation to buy the underlying asset from
the call option writer.
• Put option holder has the right but not the
obligation to sell the underlying asset to the
put option writer.
• The option holder pays the option premium
when the contract is entered.
15-16
Option Writing
• The act of selling an option
• Option writer = seller of an option
contract
• Call option writer obligated to sell the
underlying asset to the call option holder.
• Put option writer obligated to buy the
underlying asset from the put option holder.
• Option writer receives the option premium
when contract entered
15-17
17
Option Exercise
• American-style
• Exercisable at any time up to and including
the option expiration date
• European-style
• Exercisable only at the option expiration
date
• Very Important: Option holders also have the right
to sell their option at any time. That is, they do not
have to exercise the option if they no longer want it.
15-18
18
Option Payoffs & Profits
Notation:
•
•
•
•
•
•
S = current stock price per share
K = option exercise or strike price
C = call option premium per share
P = put option premium per share
“+” = Buy
“-” = Sell
15-19
19
Option Payoffs vs. Option Profits
• Initial cash flow:
• Option price = option premium
• Paid by buyer (holder) to writer
• Terminal cash flow:
• Value of option at expiration
• Option payoff
• Realized by option holder by exercising
the option.
Profit = Terminal cash flow − Initial cash flow
15-20
20
Option Payoffs & Profits
Call Holder
Payoff to Call Holder
(S - K)
if S >K
0
if S < K
= MAX(S-K,0)
Profit to Call Holder
Payoff - Option Premium
Profit =MAX(S-K, 0) - C
15-21
21
Option Payoffs & Profits
Call Writer
Payoff to Call Writer
- (S - K)
if S > K = -MAX(S-K, 0)
0
if S < K = MIN(K-S, 0)
Profit to Call Writer
Payoff + Option Premium
Profit = MIN(K-S, 0) + C
15-22
22
Call Option Payoffs
15-23
23
Call Option Profits
15-24
24
Payoff & Profit Profiles for Calls
Payoff
Profit
Call Holder
0
Call Writer
Stock Price
15-25
25
Option Payoffs and Profits
Put Holder
Payoffs to Put Holder
0
if S > K
(K - S)
if S < K
= MAX(K-S, 0)
Profit to Put Holder
Payoff - Option Premium
Profit = MAX(K-S, 0) - P
15-26
26
Option Payoffs and Profits
Put Writer
Payoffs to Put Writer
0
if S > K
-(K - S) if S < K
= -MAX(K-S, 0)
= MIN(S-K, 0)
Profits to Put Writer
Payoff + Option Premium
Profit = MIN(S-K, 0) + P
15-27
27
Put Option Payoffs
15-28
28
Put Option Profits
15-29
29
Payoff & Profit Profiles for Puts
Profits
Put Writer
0
Put Holder
Stock Price
15-30
30
Option Payoffs and Profits
CALL
PUT
Holder: Payoff
(Long) Profit
MAX(S-K,0)
MAX(S-K,0)-C
“Bullish”
MAX(K-S,0)
MAX(K-S,0)-P
“Bearish”
Writer: Payoff
(Short) Profit
MIN(K-S,0)
MIN(K-S,0)+C
“Bearish”
MIN(S-K,0)
MIN(S-K,0)+P
“Bullish”
15-31
31
Stock Index Options
• Option on a stock market index
• Cash settlement procedure
• Actual delivery of all stocks comprising a
stock index = impractical
• If option expires in the money:
• Option writer pays option holder the intrinsic
value of the option
• Cash settlement procedure same for calls
and puts
15-32
32
Stock Index Options
• American style
• OEX = S&P100 index options
• European style
• SPX = S&P500 index options
• DJX = DJIA index options
15-33
33
Index
Option
Trading
15-34
Index
Option
Trading
15-35
Stock Index Options: Example
• Suppose you bought 5 October 1500 SPX call
option contracts at a quoted price of $4.75.
(Price per SPX = 100 x quote)
• How much did you pay?
$4.75 X 5 X 100 = $2,375
• If the index is at 1520 at expiration, what would
you receive?
$100 X (1520-1500) X 5 = $10,000
15-36
36
Option Intrinsic Values
• The intrinsic value of an option = the payoff that an
option holder receives if the underlying stock price
does not change from its current value.
• If S = the current stock price, and K = the strike price:
• Call option intrinsic value = MAX [S-K,0 ]
• The call option intrinsic value is the maximum of zero or
the stock price minus the strike price.
• Put option intrinsic value = MAX [K – S, 0 ]
• The put option intrinsic value is the maximum of zero or
the strike price minus the stock price.
15-37
Option “Moneyness”
• “In-the-money” = an option that would yield a
positive payoff if exercised
• “Out-of-the-money” = an option that would
NOT yield a positive payoff if exercised
Call Option
In-theMoney
S>K
At or Out-ofthe-Money
S≤K
Put Option
S<K
S≥K
S = stock price
K = exercise price
15-38
38
Option “Moneyness”
Call Option
Strike Price = K = $25
S
(S-K) "Moneynesss"
$20
($5)
Out
$25
$0
At
$30
$5
In
Put Option
Strike Price = K = $25
S
(K-S) "Moneynesss"
$20
$5
In
$25
$0
At
$30
($5)
Out
15-39
39
Arbitrage, Intrinsic Values and Option
Pricing Bounds
• Arbitrage:
• No possibility of a loss
• A potential for a gain
• No cash outlay
• In finance, arbitrage is not allowed to persist.
• “Absence of Arbitrage” = “No Free Lunch”
• The “Absence of Arbitrage” rule is often used in
finance to calculate option prices.
15-40
Intrinsic Values and Arbitrage: Calls
• Call options with American-style exercise
must sell for at least their intrinsic value.
• Suppose: S = $60; C = $5; K = $50.
• Instant Arbitrage:
• Buy the call for $5.
• Immediately exercise the call, and buy the stock
for $50.
• In the next instant, sell the stock at the market
price of $60.
• Profit = $5 per share
American call option price = MAX[S - K, 0]
15-41
41
Intrinsic Values and Arbitrage: Puts
• Put options with American-style exercise
must sell for at least their intrinsic value.
• Suppose: S = $40; P = $5; K = $50.
• Instant Arbitrage:
• Buy the put for $5.
• Buy the stock for $40.
• Immediately exercise the put, and sell the stock
for $50.
• Profit = $5 per share profit
American put option price = MAX[K - S, 0]
15-42
42
Upper Bound for a Call Option Price
Call option price must be < stock price
• A call option is selling for $65; the underlying
stock is selling for $60.
• Arbitrage: Sell the call, Buy the stock.
• Worst case: Option is exercised; you pocket $5.
• Best case: Stock price < $65 at expiration, you
keep all of the $65.
15-43
43
Upper Bound for a European Put Option Price
European Put option price must be < strike price
• Put option with a $50 strike price is selling for $60.
• Arbitrage: Sell the put, Invest the $60
• Worse case: Stock price goes to zero
• You must pay $50 for the stock
• But, you have $60 from the sale of the put (plus
interest)
• Best case: Stock price ≥ $50 at expiration
• Put expires with zero value
• You keep the entire $60, plus interest
15-44
44
The Upper Bound for European Put
Option Prices
• Risk-free rate = 3 % per quarter.
• Put option with an exercise price of $50 and 90 days
to maturity.
• What is the maximum put value that does not result
in an arbitrage?
Maxim umput price 1.03  $50
Maxim umput price  $50/1.03  $48.54
• The maximum price for a European put option is the
present value of the strike price computed at the risk-free
rate.
15-45
Option Trading Strategies
• Type I: Add an option position to a stock position
• Helps traders modify their stock risk
• Example: Covered Calls
• Type II: Spreads.
• Two or more options of the same type (i.e., only calls
or only puts).
• Example: Butterfly Spread
 Three option positions using equally-spaced strikes
with the same expiration
15-46
Option Trading Strategies
• Type III: Combinations
• A position in a mixture of call and put options.
• Example: Straddle
• Buy one call and one put with the same strike and
expiration
There are many option trading
strategies.
Check out the CBOE’s web site.
15-47
Option Strategies
• Protective put
• Buy a put option on a stock already owned
• Protects against a decline in value
• Covered call
• Selling a call option on stock already owned
• Exchanges “upside” potential for current income.
• Straddle
• Buying or selling a call and a put with the same
exercise price.
• Buying = long straddle; selling = short straddle.
15-48
48
Protective Put
+P +S
• Limit loss; portfolio insurance
• Position - long the stock and long
the put
Payoff
Stock
Put
S≤K
S
K-S
K
S>K
S
0
S
15-49
49
Protective Put Profit
Profit
Stock
Protective Put
Portfolio
-P
S
15-50
50
Protective Put Strategy
• Suppose you own 100 shares of Microsoft
(MSFT) which you bought at the current price
of $25.00.
• You fear MSFT’s price may drop over the
next 3-months but you do not want to sell the
stock.
• Put options on MSFT with a strike price of
$24 are available.
• What will be the payoff if you buy a put
contract on MSFT?
15-51
51
Protective Put Payoffs
Payoff
If S =
Stock
Put
Payoff
S ≤ $24
$20
$20
$24 - $20
$24
S > $24
$30
$30
0
$30
15-52
52
Covered Call
+S -C
• Income enhancement; sell discipline
• Position - Own the stock and write a
call.
Payoff
Stock
Call
S≤K
S
0
S
S>K
S
- (S - K)
K
15-53
53
Covered Call Profit
Profit
Stock
Covered Call
Portfolio
-P
S
15-54
54
Covered Call Strategy
• Suppose you own 100 shares of Microsoft
(MSFT) which you bought at the current price
of $25.00.
• You expect the price to rise and you decide
to sell if the price hits $35 per share.
• Call options on MSFT with a strike price of
$35 are available.
• You decide to sell a call contract on MSFT.
• What will be your outcomes at option
expiration?
15-55
55
Covered Call Strategy
Payoff
If S =
Stock
Call
Payoff
S ≤ $35
$30
$30
0
$30
S > $35
$40
$40
-($40 -$35)
$35
15-56
56
Option Combinations: Straddle
+S–C+P
• Provides payoff if stock rises or falls
• Put and Call have the same strike
price (K) and same expiration.
Payoff
Stock (+)
Call (-)
Put (+)
S≤K
S
0
K-S
K
S>K
S
- (S - K)
0
K
15-57
57
Option Combinations: Straddle
• Suppose you own stock in a gold-mining
company called Bre-X Gold. The stock is
currently selling for $100 per share.
• Accusations have arisen about the validity of
Bre-X’s claims of finds in Australia. An
announcement is expected within a month.
• If the company’s claims are true, the stock will
increase; if they are not, it will fall dramatically.
• How can you take advantage of this?
15-58
58
Option Straddle
• If you sell a call on Bre-X with a strike
price of $100 and simultaneously buy
a put with the same strike price, your
payoff will be $100 regardless of the
news on Bre-X.
Payoff
Stock (+)
Call (-)
Put (+)
S ≤ $100
S
0
$100 - S
$100
S > $100
S
- (S - $100)
0
$100
15-59
59
Put-Call Parity
• The difference between the call price and
the put price equals the difference
between the stock price and the
discounted strike price.
• Most fundamental relationship in option
pricing
• Generally used for European-style options
15-60
60
The Put-Call Parity Formula
C  P  S  K/(1  r)
T
• Where:
•
•
•
•
•
•
C = Call option price today
S = Stock price today
r = Risk-free interest rate
P = Put option price today
K = Strike price of the put and the call
T = Time remaining until option expiration in years
Note: this formula can be
rearranged:
K/(1 r)T  S  P  C
15-61
61
Why Put-Call Parity Works
• If two securities have the same risk-less pay-off in
the future, they must sell for the same price today.
• An investor forms the following portfolio:
• Buy 100 shares of Microsoft stock
• Write one Microsoft call option contract
• Buy one Microsoft put option contract.
• At option expiration, this portfolio will be worth:
15-62
62
Put Call Parity
Disequilibrium Example
S = 110
C = 17
K = 105
P= 5
r = 10.25%
T = 0.5 yrs
C = P + S - K / (1 + r)T
17 = 5 + 110 - (105/1.05)
17  15
 Call is overpriced at 17 (should be 15)
(or Put is underpriced)
15-63
63
Put-Call Parity Arbitrage
C
Overpriced
-C
Sell the call
=
P
+ S - K/(1+r)T
-------------Underpriced ---------+P
Buy the put
+S
-PV(X)
Buy the stock
“sell the bond”
borrow at r
15-64
64
Synthetic Options
C = P + S - K / (1 + r)T
-S
Sell the stock =
=
+P
- C
Buy Put
Sell call
- K/(1+r)T
Sell bond
( borrow at r)
Synthetic
Replicate
15-65
65
Put-Call Parity with Dividends
(15.4)
C  P  S  Div  K ( 1  rf )
T
Where
“Div” = the present value of the dividend to be
paid before the option expires.
C  P  Se
 dyT
 Ke
 rT
Where dy = dividend yield on the underlying stock
15-66
66
Implied Option Prices
• Suppose a stock is currently selling for $25.
• A call option with a strike price of $30
maturing in 6 months is priced at $3.00.
• The stock will pay a dividend of $1.00 in 3
months.
• The risk-free rate is 5%.
• What is the implied price for a 6-month put
with a strike price of $30?
15-67
67
Implied Option Price
S = $25
C = $3.00
K = $30
Div = $1.00
rf = 5%
TD = 3 months = .25
T = 6 months = .5 yrs
C  P  S  Di v (1  r )TD  K (1  r )T
P  C  S  Di v (1  r )TD  K (1  r )T
P  3  25  1 (1.05)
.25
 30
(1.05).5
P  3  25  0.9879  29.277
P  $8.26
15-68
68
Why Options?
• “Why buy stock options instead of
shares in the underlying stock?”
• Compare possible outcomes from these
two investment strategies:
• Buy the underlying stock
• Buy options on the underlying stock
15-69
69
Buying the Underlying Stock
vs. Buying a Call Option
• IBM = $90 per share
• Call options = $5 per share w/$90 strike price
• Investment for 100 shares:
• IBM Shares: $9,000
• One call option contract: $500
• When the option expires in three months, the
price of IBM shares will be: $100, $80, or $90.
15-70
70
Example: Buying the Underlying Stock
versus Buying a Call Option, Cont.
Buy 100 IBM Shares
$9,000 Investment
Buy One Call Option
$500 Investment
Dollar
Profit:
Percentage
Return:
Dollar
Profit:
Percentage
Return:
Case 1: $100
$1,000
11.11%
$500
100%
Case 2: $80
-$1,000
-11.11%
-$500
-100%
Case 3: $90
$0
0%
-$500
-100%
15-71
71
Why Options? Conclusion
• Call options offer an alternative means
of formulating investment strategies:
• With call options:
•
•
•
•
Lower dollar loss potential
Lower dollar gain potential
Higher positive percentage return
Lower negative percentage return
• Insider trading venue
15-72
72
Useful Websites
•
For information on options ticker symbols, see:
•
•
•
www.schaeffersresearch.com
www.optionsxpress.com
For more information on options education:

•
To learn more about options, see:
•
•
•
•
www.optionscentral.com
www.numa.com
www.tradingmarkets.com
www.investorlinks.com
Exchanges that trade index options include:
www.cboe.com
 www.cmegroup.com

15-73