11
15
Stock Options
15-22
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
15-33
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.
15-44
Options on Common Stock
1. Identity of the underlying stock
2. Strike or Exercise price
3. Contract size
4. Expiration date or maturity
5. Exercise cycle• American or European
6. Delivery or settlement procedure
15-5
Listed Option Quotationswww.wsj.com
15-66
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
15-77
Stock Option Ticker Symbol and Strike Price Codes
15-88
Listed Option Quotes on the Web
15-9
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
15-10
“Old Style” Option Naming Convention
• “OPRA” = Options Price Reporting Authority
• 5 characters• Letters only• 3 data elements
1 2 3
Root Symbol Expiration-C-P Ind Strike Price
AAQ E D
AAQED
AAQED = call on Apple that expires in May with a $20 strike price
15-11
“New Style” Option Naming Convention
• “OCC Series Key”• 21 characters• Letters and numbers• 4 data elements
Old
1 3
Root Symbol
Exp Year
Exp Month
Exp Day Call/PutStrike Price $
Strike Price dec
AAPL 10 05 22 C 00020 000
New
AAQEDAAPL 100522C00020000
2 4
15-1212
Option Price QuotesCalls
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
15-1313
Option Price QuotesPuts
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
15-1414
Option Price Quotes
MSFT (MICROSOFT CORP) 25.98STRIKE = $25.00
CALLS Last Sale Bid Ask Vol Open IntJuly 2008 1.42 1.45 1.48 355 10472August 2008 1.80 1.85 1.87 257 927October 2008 2.36 2.43 2.46 41 3309January 2009 3.10 3.15 3.20 454 59244
PUTS Last Sale Bid Ask Vol Open IntJuly 2008 0.47 0.45 0.47 419 51464August 2008 0.81 0.80 0.82 401 1591October 2008 1.43 1.39 1.41 215 25323January 2009 2.09 2.06 2.08 2524 155877
15-1515
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.
15-16
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.
15-1717
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
15-1818
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.
15-1919
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
15-2020
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
15-2121
Payoff to Call Holder
(S - K) if S >K
0 if S < K
Profit to Call Holder
Payoff - Option Premium
Profit =MAX(S-K, 0) - C
Option Payoffs & ProfitsCall Holder
= MAX(S-K,0)
15-2222
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
Option Payoffs & ProfitsCall Writer
15-2323
Call Option Payoffs
15-2424
Call Option Profits
15-2525
Payoff & Profit Profiles for Calls
Profit
Stock Price
0
Call Writer
Call HolderPayoff
15-2626
Payoffs to Put Holder0 if S > K
(K - S) if S < K
Profit to Put Holder Payoff - Option PremiumProfit = MAX(K-S, 0) - P
Option Payoffs and Profits Put Holder
= MAX(K-S, 0)
15-2727
Payoffs to Put Writer0 if S > K = -MAX(K-S, 0)
-(K - S) if S < K = MIN(S-K, 0)
Profits to Put WriterPayoff + Option PremiumProfit = MIN(S-K, 0) + P
Option Payoffs and Profits Put Writer
15-2828
Put Option Payoffs
15-2929
Put Option Profits
15-3030
Payoff & Profit Profiles for Puts
0
Profits
Stock Price
Put Writer
Put Holder
15-3131
CALL PUT
Holder: Payoff MAX(S-K,0) MAX(K-S,0)(Long) Profit MAX(S-K,0)-C MAX(K-S,0)-P
“Bullish” “Bearish”
Writer: Payoff MIN(K-S,0) MIN(S-K,0) (Short) Profit MIN(K-S,0)+C MIN(S-K,0)+P
“Bearish” “Bullish”
Option Payoffs and Profits
15-3232
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
15-3333
Stock Index Options
• American style• OEX = S&P100 index options
• European style• SPX = S&P500 index options• DJX = DJIA index options
15-34
Index Option Trading
15-35
Index Option Trading
15-3636
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
15-37
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.
15-3838
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
In-the-Money
At or Out-of-the-Money
Call Option S > K S ≤ K
Put Option S < K S ≥ K
S = stock price K = exercise price
15-3939
Option “Moneyness”
S (S-K) "Moneynesss"$20 ($5) Out$25 $0 At$30 $5 In
S (K-S) "Moneynesss"$20 $5 In$25 $0 At$30 ($5) Out
Put OptionStrike Price = K = $25
Call OptionStrike Price = K = $25
15-40
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.
15-4141
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]
15-4242
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]
15-4343
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.
15-4444
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
15-45
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?
• The maximum price for a European put option is the present value of the strike price computed at the risk-free rate.
$48.54 $50/1.03 priceput Maximum
$50 1.03 priceput Maximum
15-46
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
15-47
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.
15-4848
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.
15-4949
Protective Put
+P +S• Limit loss; portfolio insurance• Position - long the stock and long the put
Payoff S ≤ K S > KStock S S Put K - S 0
K S
15-5050
Protective Put Profit
S
Profit
-P
Stock
Protective Put Portfolio
15-5151
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?
15-5252
Protective Put Payoffs
Payoff S ≤ $24 S > $24If S = $20 $30
Stock $20 $30Put $24 - $20 0Payoff $24 $30
15-5353
Covered Call
+S -C• Income enhancement; sell discipline• Position - Own the stock and write a call.
Payoff S ≤ K S > KStock S S Call 0 - (S - K)
S K
15-5454
Covered Call Profit
S
Profit
-P
Stock
Covered Call Portfolio
15-5555
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?
15-5656
Covered Call Strategy
Payoff S ≤ $35 S > $35If S = $30 $40
Stock $30 $40Call 0 -($40 -$35)Payoff $30 $35
15-5757
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 S ≤ K S > KStock (+) S S Call (-) 0 - (S - K)Put (+) K - S 0
K K
15-5858
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?
15-5959
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 S ≤ $100 S > $100Stock (+) S S Call (-) 0 - (S - $100)Put (+) $100 - S 0
$100 $100
15-6060
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
15-6161
The Put-Call Parity Formula
• 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
Tr)K/(1SPC
CPSr)K/(1 T Note: this formula can be rearranged:
15-6262
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:
15-6363
S = 110 K = 105 r = 10.25%C = 17 P = 5 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)
Put Call Parity Disequilibrium Example
15-6464
Put-Call Parity Arbitrage
C = P + S - K/(1+r)T
Overpriced -------------Underpriced ----------
-C +P +S -PV(X)
Sell the call Buy the put
Buy the stock
“sell the bond”
borrow at r
15-65
-S = + P - C - K/(1+r)T
Sell the stock = Buy Put Sell call Sell bond
( borrow at r)
Synthetic
Replicate
65
Synthetic Options
C = P + S - K / (1 + r)T
15-6666
Put-Call Parity with Dividends
Tf )r(KDivSPC 1(15.4)
Where
“Div” = the present value of the dividend to be paid before the option expires.
rTdyT KeSePC Where dy = dividend yield on the underlying stock
15-6767
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 $30?
15-6868
Implied Option Price
26.8$
277.299879.0253
)05.1(30)05.1(1253
)1()1(
)1()1(
5.25.
P
P
P
rKrDivSCP
rKrDivSPCTTD
TTD
S = $25 K = $30 Div = $1.00
C = $3.00 rf = 5% TD = 3 months = .25
T = 6 months = .5 yrs
15-6969
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
15-7070
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.
15-7171
Example: Buying the Underlying Stock
versus Buying a Call Option, Cont.Buy 100 IBM Shares
$9,000 InvestmentBuy 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%
15-7272
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
15-73
Useful Websites• For information on options ticker symbols, see:
• www.schaeffersresearch.com • www.optionsxpress.com
• For more information on options education: www.optionscentral.com
• To learn more about options, see:• www.numa.com • www.tradingmarkets.com • www.investorlinks.com
• Exchanges that trade index options include: www.cboe.com www.cmegroup.com
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