January 2, 2020

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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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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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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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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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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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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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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-S = -C + P – K / (1 + rt)T

15.11 Summary and Conclusions

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