Chapter 15
Stock Options
Slides
15-1. Chapter 15
15-2. Stock Options
15-3. Learning Objectives
15-4. Stock Options
15-5. Option Basics, I.
15-6. Option Basics, II.
15-7. Listed Option Quotations for Intel (INTC)
15-8. Option Price Quotes
15-9. Listed Option Quotes for Starbucks (SBUX) at Yahoo! Finance
15-10. The Options Clearing Corporation
15-11. Why Options?
15-12. Example: Buying the Underlying Stock versus Buying a Call Option
15-13. Example: Buying the Underlying Stock versus Buying a Call Option, II.
15-14. Why Options? Conclusion
15-15. Stock Index Options
15-16. Index Option Trading
15-17. Stock Index Options, Example
15-18. Option Intrinsic Values
15-19. Option “Moneyness”
15-20. More Option “Moneyness”
15-21. Option Writing
15-22. Option Exercise
15-23. Option Payoffs versus Option Profits
15-24. Call Option Payoffs
15-25. Put Option Payoffs
15-26. Call Option Profits
15-27. Put Option Profits
15-28. Credit Default Swaps, I
15-29. Credit Default Swaps, II
15-30. Using Options to Manage Risk, I.
15-31. Using Options to Manage Risk, II.
15-32. The Three Types of Option Trading Strategies
15-33. Arbitrage and Option Pricing Bounds
15-34. The Upper Bound for a Call Option Price
15-35. The Upper Bound for European Put Option Prices, I.
15-36. The Upper Bound for European Put Option Prices, II.
15-37. The Lower Bound on Option Prices
15-38. The Lower Bound on American Puts
15-39. The Lower Bounds for European Options
15-40. Put-Call Parity
15-41. The Put-Call Parity Formula
15-42. Why Put-Call Parity Works
15-43. Put-Call Parity Notes
15-44. Useful Websites
15-45. Chapter Review, I.
15-46. Chapter Review, II.
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Stock Options 15-2
Chapter Organization
15.1 Options on Common Stocks
A. Option Basics
B. Option Price Quotes
15.2 The Options Clearing Corporation
15.3 Why Options?
15.4 Stock Index Options
A. Index Options: Features and Settlement
B. Index Option Price Quotes
15.5 Option Intrinsic Value and “Moneyness”
A. Intrinsic Value for Call Options
B. Intrinsic Value for Put Options
C. Time Value
D. Three Lessons About Intrinsic Value
E. Show Me the Money
15.6 Option Payoffs and Profits
A. Option Writing
B. Option Payoffs
C. Option Payoff Diagrams
D. Option Profit Diagrams
15.7 Using Options to Manage Risk
A. The Protective Put Strategy
B. Credit Default Swaps
C. The Protective Put Strategy and Corporate Risk Management
D. Using Call Options in Corporate Risk Management
15.8 Option Trading Strategies
A. The Covered Call Strategy
B. Spreads
C. Combinations
15.9 Arbitrage and Option Pricing Bounds
A. The Upper Bound for Call Option Prices
B. The Upper Bound for Put Option Prices
C. The Lower Bounds for Call and Put Option Prices
15.10 Put-Call Parity
A. Put-Call Parity with Dividends
B. What Can We Do with Put-Call Parity?
15.11 Summary and Conclusions
Selected Web Sites
Option Exchanges:
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Stock Options 15-3
www.cboe.com
www.nyse.com
finance.yahoo.com (for option quotes)
To Learn More About Options:
www.optionsclearing.com
www.optionseducation.org
www.optionsxpress.com
www.numa.com
www.tradingmarkets.com
www.investorlinks.com
www.cboe.com/LearnCenter
www.commodityworld.com (for information on trading strategies)
www.ino.com (for information on trading options)
www.optionetics.com (to learn more about trading options)
www.optionsclearing.com (visit the OCC’s website)
Annotated Chapter Outline
15.1 Options on Common Stocks
A. Option Basics
Derivative Security: Security whose value is derived from the value of
another security. Options are a type of derivative security.
Call Option: On common stock, grants the holder the right, but not the
obligation, to buy the underlying stock at a given strike price.
Put Option: On common stock, grants the holder the right, but not the
obligation, to sell the underlying stock at a given strike price.
Strike Price: Price specified in an option contract that the holder pays to
buy shares (in the case of call options) or receives to sell shares (in the
case of put options) if the option is exercised. The strike price is also
called the striking price or the exercise price.
American Option: An option that can be exercised any time before
expiration.
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Stock Options 15-4
European Option: An option that can be exercised only at option
expiration. Note: the option “expires” on the Saturday after the third Friday
of the month. The last trading day is the third Friday of the expiration
month.
Options on common stock are a type of derivative security because the value of
the stock option is derived from the value of the underlying common stock. There
are two types of options: call options and put options.
Call options give the holder the right, but not the obligation, to purchase
the stock at a specified price for a specific period of time.
Put options give the holder the right, but not the obligation, to sell the
stock at a specified price for a specific period of time.
The specified price is the strike or exercise price, and the specific period of time
is the expiration date or option maturity. Options on common stock must stipulate
the following six contract terms:
The identity of the underlying stock.
The strike (exercise) price.
The option exercise date (option maturity).
The option contract size.
The option exercise style.
The delivery or settlement procedure.
The two basic exercise styles are American and European. Options on individual
common stocks are normally American, and options on index options are usually
European.
The standard settlement procedure for stock options requires delivery of the
underlying stock shares several days after a notice of exercise is made by the
option holder.
There are organized options exchanges and OTC markets. The largest volume of
stock options trading takes place at the Chicago Board Options Exchange
(CBOE). Other exchanges that trade stock options include: PHLX, NYSE, AMEX,
and PSE.
B. Option Price Quotes
Lecture Tip: The best way to explore option ticker symbols is through an
example where an option chain is called up online. Students can see the
relationship quite easily between the expiration month and the ticker symbol. We
summarize this, however, in Figure 15.1
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Stock Options 15-5
By convention, monthly stock options expire on the Saturday following the third
Friday of their expiration month. Weekly options expire on Fridays, with no
weekly options available the week of monthly option expiration.
Option price quotes are per share, but option contracts represent an option on
100 shares of stock, so the actual price of an option contract is 100 times the
quoted price.
Lecture Tip: Most students tend to be very interested in learning about options.
One way to stimulate this interest is to visit the CBOE website, open The Wall
Street Journal online, or use finance.yahoo.com early in the session and discuss
option price quotes. Using the WSJ as a basis for the discussion, the definitional
aspects of options can be covered, as well as option pricing. Once students
understand that an option contract that can be exercised to purchase $10,000
worth of stock sells for about $300, they become very attentive.
15.2 The Options Clearing Corporation
Options Clearing Corporation (OCC): Private agency that guarantees
that the terms of an option contract will be fulfilled if the option is
exercised; issues and clears all option contracts trading on U.S.
exchanges.
The OCC is the clearing agency for all options exchanges in the U.S., and it is
subject to regulation by the SEC. Since the OCC assumes the writer’s obligation
in all trades, all default risk is transferred to the OCC.
15.3 Why Options?
Options enable investors to effectively hold a larger position than would
otherwise be available in a straight cash stock position – i.e., leverage. Another
way to view options is that they allow an equivalent stock position for a smaller
investment.
Lecture Tip: To explain to students the benefits of purchasing stock options, visit
the CBOE website (or open The Wall Street Journal) and choose a stock option
using a specific strike price and expiration date. Hypothetically discuss the
change in option values as the stock price increases and decreases. Compare
these option values with the change in value of an investment in the underlying
stock. Calculate the percentage gains and losses on the investment in the option
and the stock investment. This will dramatically show the students the increased
leverage obtained from investing in options.
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Stock Options 15-6
15.4 Stock Index Options
In 1982, the CBOE created stock index options, which, at the time, represented a
new type of option contract.
A. Index Options: Features and Settlement
Stock Index Option: An option on a stock market index. The most
popular stock index options are options on the S&P 500 index and the
Dow Jones Industrials index.
Cash-Settled Option: An option contract settled by a cash payment
to/from the option holder when the option is exercised.
B. Index Option Price Quotes
Options are now available for a wide variety of stock market indexes. They are
quoted just as options on individual stocks.
15.5 Option Intrinsic Value and “Moneyness”
Intrinsic Value: The payoff that an option holder receives assuming the
underlying stock price remains unchanged from its current value.
The intrinsic value of an option is the payoff the option holder receives assuming
the stock price does not change from its current value. Stated alternatively, it is
the value of the option at expiration. At expiration an investor should not pay
more for the option than the value he/she would receive from buying the option
and exercising it immediately. If the investor purchased a call option, he/she
would buy the stock at the strike price and immediately sell it at the current stock
price. So the call option value would be the stock price minus the strike price. An
investor would not be able to pay less than this amount because it would be an
arbitrage opportunity. Alternatively, if an investor owned a call option at expiration
and the current stock price was less than the strike price, a rational investor
would let the option expire worthless.
If the investor purchased a put option, he/she would sell the stock at the strike
price and immediately buy it back at the current stock price. So the put option
value would be the strike price minus the stock price. An investor would not be
able to pay less than this amount because it would be an arbitrage opportunity.
Alternatively, if an investor owned a put option at expiration and the current stock
price was more than the strike price, a rational investor would let the option
expire worthless.
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Stock Options 15-7
A. The Intrinsic Value for Call Options
Call option intrinsic value = max [0, S – K]
B. The Intrinsic Value for Put Options
Put option intrinsic value = max [0, K – S]
You read the max operator as follows: The call option intrinsic value is the
maximum of zero or the value of the stock price minus the strike price.
Example for calls:
If S = 50, and K = $45, the intrinsic value of a call is:
max [0, S – K] = max [0, 50 – 45] = 5.
If S = 40 and K = $45, the intrinsic value of a call is:
max [0, S – K] = max [0, 40 – 45] = 0.
Call and put options are never less than their intrinsic values, as follows:
Call option price max [0, S – K]
Put option price max [0, K – S]
An option with a positive intrinsic value (for calls: S – K > 0) is considered “in-the-
money,” an option with a zero intrinsic value (for calls: S – K < 0) is considered
“out-of-the-money,” and an option with the stock price equal to the strike price is
considered “at-the-money.”
C. Time Value
Time (or speculative) Value: The value of an option in excess of its
intrinsic value.
D. Three Lessons About Intrinsic Value
1. Investors can calculate intrinsic value at or before expiration
2. At expiration, the value (or price) equals intrinsic value
3. Before expiration, the price is intrinsic value plus time value
E. Show Me the Money
The term “moneyness” is often used when one is describing the relation between
the strike price of an option and the price of the underlying. To understand option
payoffs and profits, we need to know two important terms related to option value:
in-the-money options and out-of-the-money options. Essentially, an in-the-money
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Stock Options 15-8
option is one that would yield a positive payoff if exercised immediately, and an
out-of-the-money option is one that would not yield a positive payoff if exercised.
An at-the-money option is one that, if exercised, would have a payoff of zero.
If the stock price, S, is greater than the strike price, K, a call option is said to be
“in the money.” In this situation, a put option is said to be “out of the money.”
Likewise, if the current stock price is less than the strike price, a call option is “out
of the money” and a put option is “in the money.” Notice that for a given strike
price, either the call or the put is in-the-money. If the stock price equals the
exercise price, an option is at-the-money.
15.6 Option Payoffs and Profits
A. Option Writing
Option Writing: Taking the seller’s side of an option contract.
Call Writer: One who has the obligation to sell stock at the option’s strike
price if the option is exercised.
Put Writer: One who has the obligation to buy stock at the option’s strike
price if the option is exercised.
The seller of an option is the writer. The option writer receives the option price
and assumes the obligation of satisfying the buyer’s exercise rights if the option
is exercised. The call writer is obligated to sell the stock at the exercise price,
and the put writer is obligated to buy the stock at the exercise price.
Lecture Tip: The previous Lecture Tip makes use of The Wall Street Journal to
show the potential profits and losses from investing in options. Now follow up
with similar examples to show how writing options provides the cash inflow of the
option premium, but involves certain risks. Show the call (put) option profits as
the price of the stock stays the same or decreases (increases), and the losses of
writing a call (put) option as the stock price increases (decreases). This may be a
good time to introduce covered versus “naked” options.
“Naked” option positions are those that do not involve an underlying asset. A
covered call position, for example, is a trading strategy that has a long stock and
short call option position. A “naked” option position would be one where the
trader just has a short call option position (or short put option position).
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Stock Options 15-9
B. Option Payoffs
The initial cash flow of an option is the option premium. The premium is a cash
outflow for the option buyer and a cash inflow for the option writer. Since buyers
and sellers have the same cash flows, options are a zero-sum game.
Lecture Tip: Students often wonder why anyone would sell an option if the only
time it is exercised is when the seller will lose money. The answer is the premium
and the fact that a majority of options are not exercised. Use the example of car
insurance, with which many students will be familiar. This is equivalent to the
insurance company selling a put.
C. Option Payoff Diagrams
The cash flows resulting from options are shown in the payoff diagrams in
Figures 15.3 and 15.4. These graphs show the cash flows from options as the
underlying stock price changes for buying and writing call and put options. The
payoff diagrams are drawn based upon the value of the option at expiration. That
is, payoff diagrams do not include the price of the option itself.
Lecture Tip: It helps to explain that the payoff diagrams are based upon cash
flows at expiration, and then show the students how the diagrams are
constructed. Explain that the option value at expiration is:
C = max(S – K, 0)
P = max(K – S, 0)
This gives students an easy method for valuing options. Now ask them to tell you
the value of the option as you vary the stock price, and plot these points on a
blank payoff diagram. Connect the points to allow students to visualize how the
payoff diagram is constructed. One can easily do this with Excel, also.
D. Option Profit Diagrams
Figures 15.5 and 15.6 are profit diagrams relating to the four basic option
investment strategies. These figures differ from Figures 15.3 and 15.4 only in that
the profit diagrams subtract the price of the original option contract and reflect the
profits resulting from the option investment.
15.7 Using Options to Manage Risk
A. The Protective Put Strategy
Protective Put: Strategy of buying a put option on stock already owned.
This protects against a decline in value.
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Stock Options 15-10
A protective put is a strategy of buying a put option on a stock already owned to
protect against a decline in value. This reduces the overall risk faced by an
investor. It can also be viewed as term insurance.
B. Credit Default Swaps
Car insurance is effectively a protective put option. In financial markets, Credit
Default Swaps (CDSs) are effectively protective puts, as they allow the holder of
the option to put (i.e., sell) the underlying asset (usually a fixed income security)
to the seller if the underlying company defaults on a debt payment.
C. The Protective Put Strategy and Corporate Risk Management
This strategy is useful for companies selling products that are subject to price
volatility.
D. Using Call Options in Corporate Risk Management
This strategy is useful for companies buying inputs that are subject to price
volatility.
Futures contracts are obligations, so while they can be used to hedge downside
risk, this comes at the expense of foregoing upside return. With options, we
retain upside, but it comes at the cost of paying the option premium. This is the
tradeoff.
15.8 Option Trading Strategies
A. The Covered Call Strategy
Covered Call: This is a strategy wherein a call option is sold on stock
already owned.
A covered call is a strategy of writing a call option on a stock already owned. This
is an alternative to the risky strategy of writing a naked option, by taking a more
conservative approach by covering the option. An investor gives up some of the
profit, and decreases the risk, in exchange for the certain option premium.
A. Spreads
Spread: An option trading strategy involving two or more call options or
two or more put options.
Bull call spreads. This spread is formed by buying a call and also
selling a call with a higher strike price.
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Stock Options 15-11
Bear call spreads. This spread is formed by buying a call and also
selling a call with a lower strike price.
Butterfly spreads. Using call options with equally spaced strikes, a
“long” butterfly spread is formed by three options positions. To
create a long butterfly spread, the trader buys one call option with
the lowest strike price, buys one call option with the highest strike
price, and sells two options with the middle strike.
B. Combinations
Combination: An option trading strategy involving two or more call and
put options.
15.9 Arbitrage and Option Pricing Bounds
An arbitrage is a trading opportunity that (1) requires no net investment on your
part, (2) has no possibility of loss, and (3) has at least the potential for a gain.
A. The Upper Bound for Call Option Prices
Logically, the most a call option can sell for is the current stock price. Otherwise
an investor would purchase the stock, rather than the option.
B. The Upper Bound for Put Option Prices
As the stock price goes up, a put option becomes less valuable, and as the stock
price decreases it becomes more valuable. So how far can the stock price
decrease to maximize the value of the put option? Obviously the stock price can
go no lower than $0. If the stock price were zero, an investor would not pay more
than the strike price for the put option because it would be impossible to recoup
their investment. The put option would not be worth less than the exercise price
because that would be an arbitrage opportunity. So the most a put option can sell
for is the strike price.
C. The Lower Bounds for Call and Put Option Prices
1. American Calls
American call option price ≥ MAX[S – K, 0]
2. American Puts
American put option price ≥ MAX[K – S, 0]
3. European Calls
European call option price ≥ MAX[S – K / (1+r)T, 0]
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Stock Options 15-12
4. European Put
European put option price ≥ MAX[K / (1+r)T – S, 0]
15.10 Put-Call Parity
Put-Call Parity: The no-arbitrage relationship between put and call prices
for European-style options with the same strike price and expiration date.
Put-Call Parity is perhaps the most fundamental relationship in option pricing.
Although put-call parity conditions exist for American options, it is much easier to
examine the put-call parity condition for options with European-style exercise.
Put-Call Parity states: the difference between the call price and the put price
equals the difference between the stock price and the discounted strike price.
The put-call parity formula is:
In the formula, C is the call option price today; S is the stock price today; r is the
risk-free interest rate; P is the put option price today; K is the strike price of the
put and the call; T is the time remaining until option expiration.
Lecture Note: Students sometimes do not grasp the fact that this is an algebraic
relationship. That is, it can be manipulated. A very handy version is:
Put-call parity is based on this fundamental of finance: If two securities have the
same risk-less pay-off in the future, they must sell for the same price today.
Example: Today, suppose an investor forms the following portfolio:
Buys 100 shares of Microsoft stock
Writes one Microsoft call option contract
Buys one Microsoft put option contract.
The net cost of this portfolio today is: S + P – C.
At option expiration, this portfolio will be worth K. (You can point out to students
that one marvel of put-call parity is that a risk-less security can be formed by a
portfolio of risky securities). Therefore, the cost of this portfolio today is:
K
(1+r)T
.
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C−P=S−K
(1+r)T
K
(1+r)T=S+P−C
Stock Options 15-13
If the portfolio had any other value, there would be an arbitrage opportunity
available.
A fun fact that emerges from put-call parity is this: Suppose S = K (and T > 0),
then C > P. That is, when options are alive, and if the options are exactly at the
money, calls are worth more than puts.
Important Note: Put-call parity is a relationship between the price of a call and
the price of a put. That is, one cannot solve for the call option price using put-call
parity—unless one has the put price. Where does one get the put price? From
put-call parity—assuming one has the call price. This circular reasoning shows
that an option pricing model must be employed to provide call option prices, in
the absence of a put option price.
A. Put-Call Parity with Dividends
The put-call parity argument stated above assumes that the underlying stock
paid no dividends before option expiration. Let’s say the stock does pay a
dividend before option expiration. First, we will rewrite the put-call parity
relationship as:
S = C – P + K / (1 + rt)T
If the stock pays a dividend, the holder of the stock will receive a dividend at
some time before option expiration. To get the same payoff, the holder of the
portfolio needs an extra amount today. Because the dividend occurs at a later
date, this extra amount is the present value of the dividend.
If the stock does pay a dividend before option expiration, then we adjust the put-
call parity equation to:
C – P = S – Div – K / (1 + rt)T
where Div is the present value of dividends to be paid during the life of the
option.
B. What Can We Do with Put-Call Parity?
Put-call parity allows us to calculate the price of a call option before it expires. To
calculate the call option price using put-call parity, however, you have to know the
price of a call option with the same strike price. If you use an option-pricing
model to calculate a call option price, you can use put-call parity to calculate a
put price.
Lecture Tip: One key use of parity is replication (or creating synthetic securities).
For example, when Facebook went public, many investors wanted to short the
stock. However, the relative lack of share availability meant high borrowing costs.
So, investors could use the option market to create a synthetic short position:
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Stock Options 15-14
-S = -C + P – K / (1 + rt)T
15.11 Summary and Conclusions
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