1. 15
Stock Options

2. Learning Objectives
In this chapter, we will discuss general features of options, but will focus on options on individual common stocks.
We will see the tremendous flexibility that options offer investors in designing investment strategies.
1. The basics of option contracts and how to obtain price quotes.
2. The difference between option payoffs and option profits.
3. The workings of some basic option trading strategies.
4. The logic behind the put-call parity condition.

3. Option Basics
A stock option is a derivative security, because the value of the option is “derived” from the value of the underlying common stock.
An option is a contract which gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time.
There are two basic financial option types.
Call options are options to buy the underlying asset. When exercising a call option, you “call in” the asset.
Put options are options to sell the underlying asset. When exercising a put, you “put” the asset to someone.
Listed option contracts are standardized to facilitate trading and price reporting.
Listed stock options give the option holder the right to buy or sell 100 shares of stock.

4. Option Basics, Cont.
Option contracts are legal agreements between two parties—the buyer of the option, and the seller of the option.
The minimum terms stipulated by stock option contracts are:
The identity of the underlying stock.
The strike price, or exercise price.
The option contract size.
The option expiration date, or option maturity.
The option exercise style (American or European).
The delivery, or settlement, procedure.
Stock options trade at organized options exchanges, such as the CBOE, as well as over-the-counter (OTC) options markets.

5. Option Vocabulary
Exercise (or strike) price: The price stated in the option contract at which the security can be bought or sold.
Option price (premium): The market price of the option contract.
Expiration date: The date the option matures.
Exercise value: The value of a call or put option if it were exercised today
EV of Call = Max (ST ─ X, 0)
EV of Put = Max (X ─ ST, 0)

6. More Terminologies
In-the-money call: A call whose exercise price is less than the current price of the underlying stock.
Out-of-the-money call: A call option whose exercise price exceeds the current stock price.
At-the-money call: A call option whose exercise price is equal to the current stock price.

7. Option Price Quotes
A list of available option contracts and their prices for a particular security is known as an option chain.
Option chains are available online through many sources, including the CBOE ( and Yahoo! Finance (
Stock option ticker symbols include:
Letters to identify the underlying stock.
A letter to identify the expiration month as well as whether the option is a call or a put. (A through L for calls; M through X for puts).
A letter to identify the strike price (a bit more complicated—see Yahoo or Stock-Trak for tables to explain this letter.)

8. The Change in Stock Option Ticker Symbols

9. Stock Option Ticker Symbol and Strike Price Codes

10. Listed Option Quotes at Yahoo! Finance

11. The Options Clearing Corporation
The Options Clearing Corporation (OCC) is a private agency that guarantees that the terms of an option contract will be fulfilled if the option is exercised.
The OCC issues and clears all option contracts trading on U.S. exchanges.
Note that the exchanges and the OCC are all subject to regulation by the Securities and Exchange Commission (SEC).
Visit the OCC at:

12. Example: Call Option
You buy the call option contract that will allow you to buy from an option seller 100 shares of IBM for $50 per share at any time during the next three months. The call option is traded at $1 for each share of underlying stock.
Exercise (or strike) price = $50
Option Price = $1
Expiration: Three months
Suppose the price of IBM share rises to $55. You can exercise your option to buy IBM share at an exercise price ($50). Thus, the exercise value is $5 ($55 - $50).

13. Example: Call Option
Suppose an IBM share will rise to $55, stay at $50 or fall to $40 per share in three months. Call price = $1
Now months
IBM spot price = $55
Exercise value = $5
Profit = $4
IBM spot price = $50
Exercise value = $0
Profit = -$1
Let’s say we have $10,000 to invest
Option A: Buy 200 shares of IBM stocks at $50 per share
Option B: Buy 100 Calls at $1 per share ($1x100x100)
If the ending price is $55,
Option A = $5 x200= $1,000 profit (10% return)
Option B = $4x100x100=$40,000 profit (400% return)
IBM spot price
$50 per share
IBM spot price = $40
Exercise value = $0
Profit = -$1

14. How do we make profits from option trading?
From the previous example, assuming that the option is in-the-money at expiration, you can buy IBM share at $50 from an option seller and sell them at current market price ($55). You just made net profit of $4 profit (= ).
Thus, the call option buyer is betting on price appreciation of the underlying assets, while the put option buyer is betting on price depreciation of the underlying assets.

15. How do we lose money from option trading?
From the previous example, suppose IBM shares never rises above $50. Then your option expires worthless, so you lose an entire option price ($1).

16. Call Option Payoffs Exercise price = $50 60 40 Buy a call 20
Option payoffs ($) 10 20 30 40 50 60 70 80 90
100
Stock price ($)
-20
-40
-60
Exercise price = $50

17. Example: Put Option
You buy the put option contract that will allow you to sell from an option seller 100 shares of IBM for $50 per share at any time during the next three months. The put option is traded at $3 for each share of underlying stock.
Exercise (or strike) price = $50
Option Price = $3
Expiration: Three months
Suppose the price of IBM share falls to $40. You can exercise your option to sell IBM share at an above-market exercise price ($50). Thus, the exercise value is $5 ($55 - $50).

18. Example: Put Option
Suppose an IBM share will rise to $55, stay at $50 or fall to $40 per share in three months. Put price = $3
Now months
IBM spot price = $55
Exercise value = $0
Profit = -$3
IBM spot price = $50
Exercise value = $0
Profit = -$3
IBM spot price
$50 per share
IBM spot price = $40
Exercise value = $10
Profit = $7

19. Put Option Payoffs 60 40 Buy a put 20 Option payoffs ($) 10 20 30 40
Option payoffs ($) 10 20 30 40 50 60 70 80 90
100
Stock price ($)
-20
-40
-60

20. Why Options?
A basic question asked by investors is: “Why buy stock options instead of shares in the underlying stock?”
To answer this question, we compare the possible outcomes from these two investment strategies:
Buy the underlying stock.
Buy options on the underlying stock.

21. Example: Buying the Underlying Stock versus Buying a Call Option
Suppose IBM is selling for $90 per share and call options with a strike price of $90 are $5 per share.
Investment for 100 shares:
IBM Shares: $9,000
One listed call option contract: $500
Suppose further that the option expires in three months.
Finally, let’s say that in three months, the price of IBM shares will either be: $100, $80, or $90.

22. Example: Buying the Underlying Stock versus Buying a Call Option, Cont.
Let’s calculate the dollar and percentage returns given each of the prices for IBM stock:
Buy 100 IBM Shares ($9000 Investment):
Buy One Call Option ($500 Investment):
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%

23. Why Options? Conclusion
Whether one strategy is preferred over another is a matter for each individual investor to decide.
That is, in some instances investing in the underlying stock will be better. In other instances, investing in the option will be better.
Each investor must weight the risk and return trade-off offered by the strategies.
It is important to see that call options offer an alternative means of formulating investment strategies.
For 100 shares, the dollar loss potential with call options is lower.
For 100 shares, the dollar gain potential with call options is lower.
The positive percentage return with call options is higher.
The negative percentage return with call options is lower.

24. Why buying financial options is very risky way to invest for individual investors?
Shorter-term investment, although LEAPs are introduced recently.
LEAPs: Long-term Equity AnticiPation securities that are similar to conventional options except that they are long-term options with maturities of up to 2 1/2 years.
High level of volatility

25. Price Volatility of Options: AOL Time Warner example

26. Bright Side of Financial Options
Definition
Hedging: A strategy to minimize exposure to unwanted risk, while still allowing to profit from investment
Suppose a portfolio manger currently holds $10 million of GOOG stocks. The investment horizon is 3-month period. In three month, she will dispose the holdings. The current market price of GOOG is $500 per share. The number of shares of current holdings is 20,000 (=10M/500) shares.
She fears of a price drop over the next 3-month period.
What can she do to minimize risk using puts?

27. No option strategy If GOOG appreciate by 20% in 3-month,
Market value of portfolio = $12M
Gain = $2M
If GOOG depreciate by 20% in 3-month,
Market value of portfolio = $8M
Loss = $2M
Expected Volatility = $4M

28. Put option strategy
Today, she buys 200 puts with X=$500, P=$10 per share.
She pays the option seller $0.2M today.
If GOOG appreciates by 20% in 3-month,
Market value of portfolio = $12M (No exercise)
Gain = $12M – 10M – 0.2M = $1.8M
If GOOG depreciates by 20% in 3-month,
Market value of portfolio = $10M (Exercise!)
Loss = $10M – 10M – 0.2M = −$0.2M (Loss)
Expected Volatility = $2M

29. Is there any scientific way to derive the price of options?
Yes. The Black-Scholes Option Pricing Model.

30. Black-Scholes Option Pricing Model
Originally developed in the early 1970s
By Black and Scholes and later refined by Merton.
Equity option, index option, foreign currency option, interest rate option, etc
Five inputs: current stock price, exercise price, risk-free rate, maturity, volatility of the underlying asset
Visit Chicago Board of Options Exchange (

31. What are the three equations that make up the OPM?

32. What is the value of the following call option according to the OPM
What is the value of the following call option according to the OPM? Assume: P = $27; X = $25; rRF = 6%; t = 0.5 years: σ2 = 0.11 (or σ = )

33. continued N(d1) = N(0.5736) = 0.7168. N(d2) = N(0.3391) = 0.6327.
Note: Values obtained from Excel using NORMSDIST function.
V = $27(0.7168) − $25e−0.03(0.6327)
= $ − $25( )(0.6327)
= $ 16

34. Black-Scholes Option Pricing Model
Stock Price (P):
$27.00
D1 =
0.5733
Exercise Price (EX):
$25.00
D2 =
0.3388
Risk-free rate (r):
0.06
N(D1) =
0.7168
Dividend Yield (d):
N(D2) =
0.6326
Time to Expiration (T):
0.5
N(-D1) =
0.2832
Standard Dev. (SD):
33.17%
N(-D2) =
0.3674
CALL PRICE =
$4.01
PUT PRICE =
$1.27
DELTA =
GAMMA =
0.0535
RHO =
7.6741
VEGA =
6.4622
THETA =

35. VIX from CBOE
The CBOE Volatility Index® (VIX®) is a key measure of market expectations of near-term volatility conveyed by S&P 500 stock index option prices. Since its introduction in 1993, VIX has been considered by many to be the world's premier barometer of investor sentiment and market volatility.
VIX shows the market's expectation of 30-day volatility. It is constructed using the implied volatilities of a wide range of S&P 500 index options. 
The VIX is a widely used measure of market risk and is often referred to as the "investor fear gauge".

36. VIX – Fear Gauge

37. What impact do the following parameters have on a call option’s value?
Current stock price: Call option value increases as the current stock price increases.
Exercise price: As the exercise price increases, a call option’s value decreases.
Option period: As the expiration date is lengthened, a call option’s value increases (more chance of becoming in the money.)
Risk-free rate: Call option’s value tends to increase as rRF increases (reduces the PV of the exercise price).
Stock return variance: Option value increases with variance of the underlying stock (more chance of becoming in the money).

38. Consider a call option with Exercise Price = $20

39. Call Premium Diagram 5 10 15 20 25 30 35 40 45 50 Option value 30 25
Market price
Exercise value
Stock Price

40. Observations
The market price of the option is almost always greater than or equal to the exercise value. Why?
The market price of the option is greater than zero even when the option is out-of-the money. Why?

41. Intrinsic Value and Speculative Value
The difference between the exercise price of the option and the spot price of the underlying asset. That is, exercise value.
Speculative Value (or Time Value)
The difference between the option price and the intrinsic value of the option.
Option Price
Intrinsic Value
Speculative Value + =

42. Example
In the earlier table, when stock price is $21, the exercise value is $1 (=21-20). However, the market value is $ Thus,
Option price
= Intrinsic value +Time value
9.75 (Option Price)
= 1 (Exercise Value ) (Time Value)

43. Stock Index Options
A stock index option is an option on a stock market index.
The most popular stock index options are options on the S&P 100, S&P 500, and Dow Jones Industrial Average.
Because the actual delivery of all stocks comprising a stock index is impractical, stock index options have a cash settlement procedure.
That is, if the option expires in the money, the option writer simply pays the option holder the intrinsic value of the option.
The cash settlement procedure is the same for calls and puts.

44. Index Option Trading, Part One

45. Index Option Trading, Part Two

46. Option “Moneyness”
“In-the-money” option: An option that would yield a positive payoff if exercised
“Out-of-the-money” option: An option that would NOT yield a positive payoff if exercised
Use the relationship between S (the stock price) and K (the strike price):
Note for a given strike price, only the call or only the put can be “in-the-money.”
In-the-Money
Out-of-the-Money
Call Option
S > K
S ≤ K
Put Option
S < K
S ≥ K

47. Option Writing
The act of selling an option is referred to as option writing.
The seller of an option contract is called the writer.
The writer of a call option contract is obligated to sell the underlying asset to the call option holder.
The call option holder has the right to exercise the call option (i.e., buy the underlying asset at the strike price).
The writer of a put option contract is obligated to buy the underlying asset from the put option holder.
The put option holder has the right to exercise the put option (i.e., sell the underlying asset at the strike price).
Because option writing obligates the option writer, the option writer receives the price of the option today from the option buyer.

48. Option Exercise
Option holders have the right to exercise their option.
If this right is only available at the option expiration date, the option is said to have European-style exercise.
If this right is available at any time up to and including the option expiration date, the option is said to have American-style exercise.
Exercise style is not linked to where the option trades. European-style and American-style options trade in the U.S., as well as on other option exchanges throughout the world.
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.

49. Option Payoffs versus Option Profits
Option investment strategies involve initial and terminal cash flows.
Initial cash flow: option price (often called the option premium).
Terminal cash flow: the value of an option at expiration (often called the option payoff.
The terminal cash flow can be realized by the option holder by exercising the option.
Option Profits = Terminal cash flow − Initial cash flow

50. Call Option Payoffs

51. Put Option Payoffs

52. Call Option Profits

53. Put Option Profits

54. Using Options to Manage Risk, I.
Protective put - Strategy of buying put options to protect against falling values.
Protective puts provide “insurance” for the value of an asset or a stream of cash inflows.

55. Using Options to Manage Risk, II.
Protective call - Strategy of buying call options to protect against rising prices.
Protective calls provide a way to “lock-in” the value of a liability or a stream of cash outflows.

56. The Three Types of Option Trading Strategies
Type I: Traders add an option position to their stock position.
These strategies help traders modify their stock risk.
Example: Covered Calls (Selling a call option on a stock already owned).
Type II: Spreads.
A position with 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.
Buy one call option with the lowest strike.
Buy one call option with the highest strike.
Sell two call options with the middle strike.
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.

57. Option Intrinsic Values
The intrinsic value of an option is the payoff that an option holder receives if the underlying stock price does not change from its current value.
That is, if S is the current stock price, and K is the strike price of the option:
Call option intrinsic value = MAX [0, S – K ]
In words: The call option intrinsic value is the maximum of zero or the stock price minus the strike price.
Put option intrinsic value = MAX [0, K – S ]
In words: The put option intrinsic value is the maximum of zero or the strike price minus the stock price.

58. More Option “Moneyness”
“In the Money” options have a positive intrinsic value.
For calls, the strike price is less than the stock price.
For puts, the strike price is greater than the stock price.
“Out of the Money” options have a zero intrinsic value.
For calls, the strike price is greater than the stock price.
For puts, the strike price is less than the stock price.
“At the Money” options is a term used for options when the stock price and the strike price are about the same.

59. Arbitrage and Option Pricing Bounds
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.
Think about what would happen if arbitrage were allowed to persist. (Easy money for everybody)

60. The Upper Bound for a Call Option Price
Call option price must be less than the stock price.
Otherwise, arbitrage will be possible.
How?
Suppose you see a call option selling for $65, and the underlying stock is selling for $60.
The Arbitrage: sell the call, and buy the stock.
Worst case? The option is exercised and you pocket $5.
Best case? The stock sells for less than $65 at option expiration, and you keep all of the $65.
Zero cash outlay today, no possibility of loss, and potential for gain.

61. The Upper Bound for European Put Option Prices, I.
European put option price must be less than the strike price.
Suppose a put option with a strike price of $50 is selling for $50.
The Arbitrage: Sell the put, and invest the $50 in the bank. (Note you have zero cash outlay).
Worse case? Stock price goes to zero.
You must pay $50 for the stock (because you were the put writer).
But, you have $50 from the sale of the put (plus interest).
Best case? Stock price is at least $50 at expiration.
The put expires with zero value (and you are off the hook).
You keep the entire $50, plus interest.
So, we see that if the put option price equals the strike price, there is an arbitrage.

62. The Upper Bound for European Put Option Prices, II.
There will be an arbitrage if price of the put, plus the interest you could earn over the life of the option, is greater than the stock price.
For example, suppose the risk-free rate is 3 percent per quarter.
We have a 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?
Notice that the answer, $48.54, is the present value of the strike price computed at the risk-free rate.
Therefore: The maximum price for a European put option is the present value of the strike price computed at the risk-free rate.

63. The Lower Bound on Option Prices
Option prices must be at least zero.
An option holder can simply discard the option.
This means that no one would pay someone to take an option off their hands.
Therefore, the price of the option cannot be negative.
American Calls. Can an American call sell for less than its intrinsic value? No.
Suppose S = $60, and a call option has a strike price of K = $50 and a price of $5.
The $5 call price is less than the intrinsic value of S - K = $10.
The Arbitrage Strategy:
Buy the call option at its price of C = $5.
Immediately exercise the call option and buy the stock at K = $50.
Then, sell the stock at the current market price of S = $60.
Therefore, an American call option price is never less than its intrinsic value.
American call option price = MAX[S - K, 0]

64. The Lower Bound on American Puts
Can an American put sell for less than its intrinsic value? No.
Suppose S = $40, and a put option has a strike price of K = $50 and a price of $5.
The $5 put price is less than the intrinsic value of K - S = $10.
The Arbitrage Strategy:
Buy the put option at its price of P = $5.
Buy the stock at its price of S = $40.
Immediately exercise the put option and sell the stock at K = $50.
Therefore, an American put option price is never less than its intrinsic value.
American put option price = MAX[K - S, 0]

65. The Lower Bounds for European Options
European Calls. European options cannot be exercised before expiration.
Therefore, we cannot use the arbitrage strategies to set lower bounds for American options.
We must use a different approach (which can easily be found).
The lower bound for a European call option is greater than its intrinsic value.
European call option price ≥ MAX[S - K/(1 + r)T, 0]
European Puts. The lower bound for a European put option price is less than its intrinsic value.
In fact, in-the-money European puts will frequently sell for less than their intrinsic value. How much less?
Using an arbitrage strategy that accounts for the fact that European put options cannot be exercised before expiration:
European put option price ≥ MAX[K/(1 + r)T – S, 0]

66. Put-Call Parity
Put-Call Parity is perhaps the most fundamental relationship in option pricing.
Put-Call Parity is generally used 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.

67. The Put-Call Parity Formula
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
Note: this formula
can be rearranged:

68. 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.
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.
At option expiration, this portfolio will be worth:

69. Put-Call Parity Notes
Notice that the portfolio is always worth $K at expiration. That is, it is riskless.
Therefore, the value of this portfolio today is $K/(1+r)T.
That is, to prevent arbitrage: today’s cost of buying 100 shares and buying one put (net of the proceeds of writing one call), should equal the price of a risk-less security with a face value of $K, and a maturity of T.
Fun fact: If S = K (and if r > 0), then C > P.

70. Useful Websites For information on options ticker symbols, see:
For more information on options education:
To learn more about options, see:
Exchanges that trade index options include:

71. Chapter Review, I. Options on Common Stocks
Option Basics
Option Price Quotes
The Options Clearing Corporation
Why Options?
Stock Index Options
Features and Settlement
Index Option Price Quotes
Option “Moneyness”
Option Payoffs and Profits
Option Writing
Option Payoffs
Payoff Diagrams
Option Profits

72. Chapter Review, II. Using Options to Manage Risk
The Three Types of Option Trading Strategies
Adding Options to a Stock Position
Combinations
Spreads
Option Intrinsic Values
Option Prices, Intrinsic Values, and Arbitrage
The Upper Bound for a Call Option Price
The Upper Bound for a Put Option Price
The Lower Bounds on Option Prices
Put-Call Parity

73. Quiz

74. Suppose you want to buy the right to BUY 100 shares of IBM with a $140 anytime between now and July (i.e., the Option 4 from the table). Evaluate your potential gains and losses at option expiration for stock prices of $120, $140, and $160.
Stock price gain/loss ($) gains/loss (%)
$ %
$ %
$ %

75. Stock Gain/Loss ($) Gain/Loss (%) $120 1725 627% $140 -275 -100%
Given information in question 5, conduct the same analysis for IBM 140 July PUT options.
Stock Gain/Loss ($) Gain/Loss (%)
$ %
$ %
$ %

76. Suppose you are Mark Cuban, Jr
Suppose you are Mark Cuban, Jr. who is currently holding 100,000 shares of IBM. Today, the market price of IBM shares is $$138.25, as shown in the table. You fear of growing volatility of IBM share prices and want to hedge against falling share prices for next several months ending August 2004 (i.e., the Option 5 from the table). What would you do using options on stocks available above? Be sure to identify the number of options contracts to be bought, the options premium, and expiration months. Suppose an IBM share price in August 2004 when the options expire is $100. Calculate net gain or loss from your strategy using options contracts. In your calculation, include gains or losses from the market value change in your holding of IBM shares.