stock options

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

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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.

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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

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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

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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

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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

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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

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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.

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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

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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.

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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

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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

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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)

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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

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Call Option Payoffs

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Call Option Profits

15-2525

Payoff & Profit Profiles for Calls

Profit

Stock Price

0

Call Writer

Call HolderPayoff

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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)

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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

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Put Option Payoffs

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Put Option Profits

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Payoff & Profit Profiles for Puts

0

Profits

Stock Price

Put Writer

Put Holder

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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

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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

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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

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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.

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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

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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.

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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]

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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]

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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.

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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

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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.

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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.

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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

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Protective Put Profit

S

Profit

-P

Stock

Protective Put Portfolio

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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?

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Protective Put Payoffs

Payoff S ≤ $24 S > $24If S = $20 $30

Stock $20 $30Put $24 - $20 0Payoff $24 $30

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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

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Covered Call Profit

S

Profit

-P

Stock

Covered Call Portfolio

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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?

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Covered Call Strategy

Payoff S ≤ $35 S > $35If S = $30 $40

Stock $30 $40Call 0 -($40 -$35)Payoff $30 $35

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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

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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?

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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

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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

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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:

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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

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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

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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.

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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%

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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

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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