1 Chapter 17 Principles of Options and Option Pricing Portfolio Construction, Management, & Protection, 5e, Robert A. Strong Copyright ©2009 by South-Western, a division of Thomson Business & Economics. All rights reserved.

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, on his journal article with Myron Scholes that gave birth to the Black-Scholes Option Pricing Model

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

4 Why Options Are a Good Idea u Options: 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 u The investment process is dynamic: The portfolio manager needs to constantly reassess and adjust portfolios with the arrival of new information u Options are more convenient and less expensive than wholesale purchases or sales of stock

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

6 Practical Example of a Call Option

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

8 Standardized Option Characteristics u 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

9 Standardized Option Characteristics (cont’d) u 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

10 Standardized Option Characteristics (cont’d) u 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

11 Where Options Come From u If you buy an option, someone has to sell it to you u No set number of put or call options exists The number of options in existence changes every day Option can be created and destroyed

12 Opening and Closing Transactions u 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

13 Opening and Closing Transactions (cont’d) u 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

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

15 Role of the Options Clearing Corporation u 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

16 OCC-Related Information on the Web

17 Where and How Options Trade u In the United States, options trade on five principal exchanges: Chicago Board Options Exchange (CBOE) American Stock Exchange (AMEX) Philadelphia Stock Exchange Pacific Stock Exchange International Securities Exchange

18 Where and How Options Trade (cont’d) u 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

19 Where and How Options Trade (cont’d) u 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

20 Where and How Options Trade (cont’d) u 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

21 Intrinsic Value and Time Value u Option “prices” are referred to as option “premiums” u 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

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

23 The Financial Page Listing u 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

24 The Financial Page Listing

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

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

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

28 Option Exercise u 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 u European options can be exercised only at expiration

29 Exercise Procedures u 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 down payment on the option terms

30 Exercise Procedures (cont’d) u 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

31 Exercise Procedures (cont’d) u 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

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

33 Profit and Loss Diagrams (cont’d) u For the Disney JUN Call writer: $0.25 $22.50 $0 Maximum profit Breakeven Point = $22.75 Maximum loss is unlimited

34 Profit and Loss Diagrams (cont’d) u For the Disney JUN Put buyer: -$1.05 $22.50 $0 Maximum loss Breakeven Point = $21.45 Maximum profit = $21.45

35 Profit and Loss Diagrams (cont’d) u For the Disney JUN Put writer: $1.05 $22.50 $0 Maximum profit Breakeven Point = $21.45 Maximum loss = $21.45

36 Option Pricing u Determinants of the Option Premium Market Factors & Accounting Factors u Black-Scholes Option Pricing Model u Development and Assumptions of the Model u Insights into the Black-Scholes Model u Delta u Theory of Put/Call Parity u Stock Index Options

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

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

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

40 Accounting Factors u 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 striking price is reduced by the split ratio –The number of shares covered by your options is increased by the split ratio

41 Black-Scholes Option Pricing Model u The Black-Scholes OPM:

42 Black-Scholes Option Pricing Model (cont’d) u 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

43 Black-Scholes Option Pricing Model (cont’d) u 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)

44 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 According to the Black-Scholes OPM, what should be the premium for this option?

45 Black-Scholes Option Pricing Model (cont’d) Example (cont’d) Solution: We must first determine d 1 and d 2 :

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

47 Black-Scholes Option Pricing Model (cont’d) Example (cont’d) Solution (cont’d): The next step is to find the normal probability values for d 1 and d 2. Using Microsoft Excel’s NORMSDIST function yields:

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

49 Using Microsoft Excel’s NORMSDIST Function u The Excel portion below shows the input and the result of the function:

50 Development and Assumptions of the Model u Many of the steps used in building the Black-Scholes OPM come from: Physics Mathematical shortcuts Arbitrage arguments u The actual development of the OPM is complicated

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

52 The Stock Pays No Dividends during the Option’s Life (cont’d) u 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

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

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

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

56 Constant Interest Rates u The OPM assumes that the interest rate R in the model is known and constant u 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

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

58 Insights into the Black-Scholes Model u Divide the OPM into two parts: Part APart B

59 Insights into the Black-Scholes Model (cont’d) u 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(d 1 ) 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

60 Insights into the Black-Scholes Model (cont’d) u Part B is the present value of the exercise price on the expiration day: N(d 2 ) is the actual probability the option will be in the money on expiration day

61 Insights into the Black-Scholes Model (cont’d) u 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

62 Delta u Delta is the change in option premium expected from a small change in the stock price, all other things being the same:

63 Delta (cont’d) u Delta allows us to determine how many options are needed to mimic the returns of the underlying stock u Delta is exactly equal to N(d 1 ) e.g., if N(d 1 ) 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

64 Theory of Put/Call Parity u 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

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

66 Stock Index Options u Stock index options are the option exchanges’ most successful innovation e.g., the S&P 100 index option u Index options have no delivery mechanism All settlements are in cash

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