1. Chapter 17 Principles of Options and Option Pricing

2. We sent the first draft of our paper to the Journal of Political Economy and promptly got back a rejection letter. We then sent it to the Review of Economics and Statistics, where it was also rejected.
Merton Miller and Eugene Fama…then took an interest in the paper and gave us extensive comments on it. They suggested to the JPE that perhaps the paper was worth more serious consideration. The journal then accepted the paper.
- Fischer Black

3. Outline
Introduction
Option principles
Option pricing

4. Introduction
Innovations in stock options have been among the most important developments in finance in the last 20 years
The cornerstone of option pricing is the Black-Scholes Option Pricing Model (OPM)
Delta is the most important OPM progeny to the portfolio manager

5. Option Principles Why options are a good idea What options are
Standardized option characteristics
Where options come from
Where and how options trade
The option premium
Sources of profits and losses with options

6. Why Options Are A Good Idea
Give the marketplace opportunities to adjust risk or alter income streams that would otherwise not be available
Provide financial leverage
Can be used to generate additional income from investment portfolios

7. Why Options Are A Good Idea (cont’d)
The investment process is dynamic:
The portfolio managers needs to constantly reassess and adjust portfolios with the arrival of new information
Options are more convenient and less expensive than wholesale purchases or sales of stock

8. What Options Are
Call options
Put options

9. Call Options
A call option gives you the right to buy within a specified time period at a specified price
The owner of the option pays a cash premium to the option seller in exchange for the right to buy

10. Practical Example of A Call Option

11. Put Options
A put option gives you the right to sell within a specified time period at a specified price
It is not necessary to own the asset before acquiring the right to sell it

12. Standardized Option Characteristics
All exchange-traded options have standardized expiration dates
The Saturday following the third Friday of designated months for most options
Investors typically view the third Friday of the month as the expiration date

13. Standardized Option Characteristics (cont’d)
The striking price of an option is the predetermined transaction price
In multiples of $2.50 (for stocks priced $25.00 or below) or $5.00 (for stocks priced higher than $25.00)
There is usually at least one striking price above and one below the current stock price

14. Standardized Option Characteristics (cont’d)
Puts and calls are based on 100 shares of the underlying security
The underlying security is the security that the option gives you the right to buy or sell
It is not possible to buy or sell odd lots of options

15. Where Options Come From
Introduction
Opening and closing transactions
Role of the Options Clearing Corporation

16. Introduction If you buy an option, someone has to sell it to you
No set number of put or call options exists
The number of options in existence changes every day
Option can be created and destroyed

17. Opening and Closing Transactions
The first trade someone makes in a particular option is an opening transaction
An opening transaction that is the sale of an option is called writing an option

18. Opening and Closing Transactions (cont’d)
The trade that terminates a position by closing it out is a closing transaction
Options have fungibility
Market participants can reverse their positions by making offsetting trades
E.g., the writer of an option can close out the position by buying a similar one

19. Opening and Closing Transactions (cont’d)
The owner of an option will ultimately:
Sell it to someone else
Let it expire or
Exercise it

20. Role of the Options Clearing Corporation
The Options Clearing Corporation (OCC):
Positions itself between every buyer and seller
Acts as a guarantor of all option trades
Regulates the trading activity of members of the various options exchanges
Sets minimum capital requirements
Provides for the efficient transfer of funds among members as gains or losses occur

21. OCC-Related Information on the Web

22. Where and How Options Trade
Options trade on four principal exchanges:
Chicago Board Options Exchange (CBOE)
American Stock Exchange (AMEX)
Philadelphia Stock Exchange
Pacific Stock Exchange

23. Where and How Options Trade (cont’d)
AMEX and Philadelphia Stock Exchange options trade via the specialist system
All orders to buy or sell a particular security pass through a single individual (the specialist)
The specialist:
Keeps an order book with standing orders from investors and maintains the market in a fair and orderly fashion
Executes trades close to the current market price if no buyer or seller is available

24. Where and How Options Trade (cont’d)
CBOE and Pacific Stock Exchange options trade via the marketmaker system
Competing marketmakers trade in a specific location on the exchange floor near the order book official
Marketmakers compete against one another for the public’s business

25. Where and How Options Trade (cont’d)
Any given option has two prices at any given time:
The bid price is the highest price anyone is willing to pay for a particular option
The asked price is the lowest price at which anyone is willing to sell a particular option

26. The Option Premium Intrinsic value and time value
The financial page listing

27. Intrinsic Value and Time Value
The price of an option has two components:
Intrinsic value:
For a call option equals the stock price minus the striking price
For a put option equals the striking price minus the stock price
Time value equals the option premium minus the intrinsic value

28. Intrinsic Value and Time Value (cont’d)
An option with no intrinsic value is out of the money
An option with intrinsic value is in the money
If an option’s striking price equals the stock price, the option is at the money

29. The Financial Page Listing
The following slide shows an example from the online edition of the Wall Street Journal:
The current price for a share of Disney stock is $21.95
Striking prices from $20 to $25 are available
The expiration month is in the second column
The option premiums are provided in the “Last” column

30. The Financial Page Listing

31. The Financial Page Listing (cont’d)
Investors identify an option by company, expiration, striking price, and type of option:
Disney JUN Call
Company
Expiration
Striking
Price
Type

32. The Financial Page Listing (cont’d)
The Disney JUN Call is out of the money
The striking price is greater than the stock price
The time value is $0.25
The Disney JUN Put is in the money
The intrinsic value is $ $21.95 = $0.55
The time value is $ $0.55 = $0.50

33. The Financial Page Listing (cont’d)
As an option moves closer to expiration, its time value decreases
Time value decay
An option is a wasting asset
Everything else being equal, the value of an option declines over time

34. Sources of Profits and Losses With Options
Option exercise
Exercise procedures

35. Option Exercise
An American option can be exercised at any time prior to option expiration
It is typically not advantageous to exercise prior to expiration since this amount to foregoing time value
European options can be exercised only at expiration

36. Exercise Procedures
The owner of an option who decides to exercise the option:
Calls her broker
Must put up the full contract amount for the option
The premium is not a downpayment on the option terms

37. Exercise Procedures (cont’d)
The option writer:
Must be prepared to sell the necessary shares to the call option owner
Must be prepared to buy shares of stock from the put option owner

38. Exercise Procedures (cont’d)
In general, you should not buy an option with the intent of exercising it:
Requires two commissions
Selling the option captures the full value contained in an option

39. Profit and Loss Diagrams
For the Disney JUN Call buyer:
Maximum profit
is unlimited
Breakeven Point = $22.75 $0
-$0.25
Maximum loss
$22.50

40. Profit and Loss Diagrams
For the Disney JUN Call writer:
Maximum profit
Breakeven Point = $22.75
$0.25 $0
Maximum loss
is unlimited
$22.50

41. Profit and Loss Diagrams
For the Disney JUN Put buyer:
Maximum profit = $21.45
Breakeven Point = $21.45 $0
-$1.05
Maximum loss
$22.50

42. Profit and Loss Diagrams
For the Disney JUN Put writer:
Maximum profit
Breakeven Point = $21.45
$1.05 $0
Maximum loss = $21.45
$22.50

43. Option Pricing Determinants of the option premium
Black-Scholes Option Pricing Model
Development and Assumptions of the model
Insights into the Black-Scholes Model
Delta
Theory of put/call parity
Stock index options

44. Determinants of the Option Premium
Market factors
Accounting factors

45. Market Factors Striking price Time to expiration
For a call option, the lower the striking price, the higher the option premium
Time to expiration
For both calls and puts, the longer the time to expiration, the higher the option premium

46. Market Factors (cont’d)
Current stock price
The higher the stock price, the higher the call option premium and the lower the put option premium
Volatility of the underlying stock
The great the volatility, the higher the call and put option premium

47. Market Factors (cont’d)
Dividend yield on the underlying stock
Companies with high dividend yields have a smaller call option premium than companies with low dividend yields
Risk-free interest rate
The higher the risk-free rate, the higher the call option premium

48. Accounting Factors Stock splits:
The OCC will make the following adjustments:
The striking price is reduced by the split ratio
The number of options is increased by the split ratio
For odd-lot generating splits:
The number of shares covered by your options is increased by the split ratio

49. Black-Scholes Option Pricing Model
The Black-Scholes OPM:

50. Black-Scholes Option Pricing Model (cont’d)
Variable definitions:
C = theoretical call premium
S = current stock price
t = time in years until option expiration
K = option striking price
R = risk-free interest rate

51. Black-Scholes Option Pricing Model (cont’d)
Variable definitions (cont’d):
= standard deviation of stock returns
N(x) = probability that a value less than “x” will occur in a standard normal distribution
ln = natural logarithm
e = base of natural logarithm (2.7183)

52. Black-Scholes Option Pricing Model (cont’d)
Example
Stock ABC currently trades for $30. A call option on ABC stock has a striking price of $25 and expires in three months. The current risk-free rate is 5%, and ABC stock has a standard deviation of 0.45.
According to the Black-Scholes OPM, but should be the call option premium for this option?

53. Black-Scholes Option Pricing Model (cont’d)
Example (cont’d)
Solution: We must first determine d1 and d2:

54. Black-Scholes Option Pricing Model (cont’d)
Example (cont’d)
Solution (cont’d):

55. Black-Scholes Option Pricing Model (cont’d)
Example (cont’d)
Solution (cont’d): The next step is to find the normal probability values for d1 and d2. Using Excel’s NORMSDIST function yields:

56. Black-Scholes Option Pricing Model (cont’d)
Example (cont’d)
Solution (cont’d): The final step is to calculate the option premium:

57. Using Excel’s NORMSDIST Function
The Excel portion below shows the input and the result of the function:

58. Development and Assumptions of the Model
Introduction
The stock pays no dividends during the option’s life
European exercise terms
Markets are efficient
No commissions
Constant interest rates
Lognormal returns

59. Introduction
Many of the steps used in building the Black-Scholes OPM come from:
Physics
Mathematical shortcuts
Arbitrage arguments
The actual development of the OPM is complicated

60. The Stock Pays no Dividends During the Option’s Life
The OPM assumes that the underlying security pays no dividends
Valuing securities with different dividend yields using the OPM will result in the same price

61. The Stock Pays no Dividends During the Option’s Life
The OPM can be adjusted for dividends:
Discount the future dividend assuming continuous compounding
Subtract the present value of the dividend from the stock price in the OPM
Compute the premium using the OPM with the adjusted stock price

62. European Exercise Terms
The OPM assumes that the option is European
Not a major consideration since very few calls are ever exercised prior to expiration

63. Markets Are Efficient
The OPM assumes markets are informationally efficient
People cannot predict the direction of the market or of an individual stock

64. No Commissions
The OPM assumes market participants do not have to pay any commissions to buy or sell
Commissions paid by individual can significantly affect the true cost of an option
Trading fee differentials cause slightly different effective option prices for different market participants

65. Constant Interest Rates
The OPM assumes that the interest rate R in the model is known and constant
It is common use to use the discount rate on a U.S. Treasury bill that has a maturity approximately equal to the remaining life of the option
This interest rate can change

66. Lognormal Returns
The OPM assumes that the logarithms of returns of the underlying security are normally distributed
A reasonable assumption for most assets on which options are available

67. Insights Into the Black-Scholes Model
Divide the OPM into two parts:
Part A
Part B

68. Insights Into the Black-Scholes Model (cont’d)
Part A is the expected benefit from acquiring the stock:
S is the current stock price and the discounted value of the expected stock price at any future point
N(d1) is a pseudo-probability
It is the probability of the option being in the money at expiration, adjusted for the depth the option is in the money

69. Insights Into the Black-Scholes Model (cont’d)
Part B is the present value of the exercise price on the expiration day:
N(d2) is the actual probability the option will be in the money on expiration day

70. Insights Into the Black-Scholes Model (cont’d)
The value of a call option is the difference between the expected benefit from acquiring the stock and paying the exercise price on expiration day

71. Delta
Delta is the change in option premium expected from a small change in the stock price, all other things being equal:

72. Delta (cont’d)
Delta allows us to determine how many options are needed to mimic the returns of the underlying stock
Delta is exactly equal to N(d1)
E.g., if N(d1) is 0.836, a $1 change in the price of the underlying stock price leads to a change in the option premium of 84 cents

73. Theory of Put/Call Parity
The following variables form an interrelated securities complex:
Price of a put
Price of a call
The value of the underlying stock
The riskless rate of interest
If put/call parity does not hold, arbitrage is possible

74. Theory of Put/Call Parity (cont’d)
The put/call parity relationship:

75. Stock Index Options
A stock index option is the option exchanges most successful innovation
E.g., the S&P 100 index option
Index options have no delivery mechanism
All settlements are in cash

76. Stock Index Options (cont’d)
The owner of an in-the-money index call receives the difference between the closing index level and the striking price
The owner of an in-the-money index put receives the difference between the striking price and the index level