15 Stock Options.

15 Stock Options

Option Basics Stock option = derivative security
Value “derived” from the value of the underlying common stock (underlying asset) Exchange-traded Option Contracts Standardized Facilitates trading and price reporting. Contract = 100 shares of stock Zero-sum game 2

Put and Call Options Call option Put option
Gives holder the right but not the obligation to buy the underlying asset at a specified price at a specified time. Put option Gives the holder the right but not the obligation to sell the underlying asset at a specified price at a specified time. A call option gives the holder the right but not the obligation to buy the underlying asset at a specified price at a specified time. A put option gives the holder the right but not the obligation to sell the underlying asset at a specified price at a specified time. The key words in both definitions are “the right but not the obligation.” The buyer of an option contract has the “option” to complete the purchase or sale at the specified price or not. 3

Options on Common Stock
Identity of the underlying stock Strike or Exercise price Contract size Expiration date or maturity Exercise cycle American or European Delivery or settlement procedure Let’s review the basic elements of an option: Since we’re focusing on stock options, we have to know the identity of the underlying stock. An option has a strike or exercise price which is the price that will be paid or received if the option is exercised. For stock options, the contract size is 100 shares though option prices are quoted on a per share basis. Options are typically short term instruments with maturities less than one year. Option expiration months are determined by the listing exchange. “Exercise cycle” refers to the type of option – American or European, which has nothing to do with America or Europe. American options can be exercised anytime prior to expiration; European options can be exercised only at expiration. The majority of stock options are American in style. Finally, we need to know the delivery or settlement procedure. For options on common stock, delivery is to deliver the underlying stock, Options on stock indexes are “cash-settled” since it would not be reasonable to deliver all the stocks in the S&P500 for example. 4

Listed Option Quotations www.wsj.com

Option Price Quotes Option Chain: Stock option ticker symbols include:
List of available option contracts and prices for a particular security Stock option ticker symbols include: Letters identify underlying stock Letter identifies expiration month & call/put A through L for calls; M through X for puts Letter identifies strike price 6

Stock Option Ticker Symbol and Strike Price Codes
7

Listed Option Quotes on the Web
8

Option Naming Convention Changes
Instituted by the Options Clearing Corporation Length increased from 5 to 21 characters New style includes letters and numbers Old style presented difficulties: Hard to use for Nasdaq stocks Hard for investors to interpret Proliferation of new option types

“Old Style” Option Naming Convention
“OPRA” = Options Price Reporting Authority 5 characters Letters only 3 data elements

“New Style” Option Naming Convention
“OCC Series Key” 21 characters Letters and numbers 4 data elements

Option Price Quotes Calls
The table above recaps call options on Microsoft stock expiring in July 2008. Microsoft closed at $25.98 on this trading day. Notice that options are available for July expiration with strike prices varying from $15 to $27.50 (and more actually) at intervals of $2.50.’ As we’ve seen previously, we have the last sale or closing price, both bid and ask prices, daily volume and open interest. These are call options, giving the buyer or holder the right – but not the obligation – to buy Microsoft stock at the strike price. Not surprisingly, as the strike price on a call declines, the price of the option rises. It’s more valuable to be able to buy the stock at a lower strike price. 12

Option Price Quotes Puts
This table gives put prices for Microsoft stock options expiring in July 2008. Though similar to the table on the previous slide, notice that with puts, the price of the option increases as the strike price increases. Again, this is not surprising since a put gives the holder the right to sell stock at the strike price. 13

Option Price Quotes These two small tables recap Calls and Puts on Microsoft with a strike price of $25.00 for 4 expiration months. In this case, notice that as the time to maturity increases, the price of the options also increase for both puts and calls. Again, this makes sense since the more time before the option expires, the more chance for it the price of the underlying stock to move to a point to make exercising the option profitable. 14

The Options Clearing Corporation
Private agency Guarantees contract fulfillment “Buyer to every seller; seller to every buyer” Issues and clears all option contracts trading on U.S. exchanges Subject to regulation by the Securities and Exchange Commission (SEC) Visit the OCC at: 15

Buying an Option Option holder = buyer of an option contract
Call option holder has the right but not the obligation to buy the underlying asset from the call option writer. Put option holder has the right but not the obligation to sell the underlying asset to the put option writer. The option holder pays the option premium when the contract is entered.

Option Writing The act of selling an option
Option writer = seller of an option contract Call option writer obligated to sell the underlying asset to the call option holder. Put option writer obligated to buy the underlying asset from the put option holder. Option writer receives the option premium when contract entered 17

Option Exercise American-style European-style
Exercisable at any time up to and including the option expiration date European-style Exercisable only at the option expiration date 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. 18

Option Payoffs & Profits
Notation: S = current stock price per share K = option exercise or strike price C = call option premium per share P = put option premium per share “+” = Buy “-” = Sell As we go forward, looking at various aspects of options and option trading strategies, we’ll be using the notation shown on the slide. S will indicate the current stock price per share. K will indicate the strike or exercise price. C will represent the call option price or premium on a per share basis. P will represent the put option price or premium on a per share basis. A plus sign indicates “buy.” A minus signs means “sell.” For example, “+S-C” (read “plus S minus C”) means buy the stock and sell the call. 19

Option Payoffs vs. Option Profits
Initial cash flow: Option price = option premium Paid by buyer (holder) to writer Terminal cash flow: Value of option at expiration Option payoff Realized by option holder by exercising the option. Profit = Terminal cash flow − Initial cash flow 20

Option Payoffs & Profits Call Holder
Payoff to Call Holder (S - K) if S >K 0 if S < K Profit to Call Holder Payoff - Option Premium Profit =MAX(S-K, 0) - C = MAX(S-K,0) Before we look at how to use options, we need to understand how they work – meaning what are the payoffs and profits to the buyers or holders and sellers or writers of calls and puts. We’ll start with the payoff and profit to the holder of a call option. Regardless of the ending stock price, the payoff to the holder of a call can never be less than zero. If the option is worthless, it won’t be exercised. If the stock price is above the exercise price at expiration, then the payoff is simply the stock price minus the strike price (S-K). We have to account for the premium we paid for the option contract so our net profit equals the payoff minus that premium. The payoff to a call holder can never be negative, but the profit (or loss) can be negative but never more than the premium. 21

Option Payoffs & Profits Call Writer
Payoff to Call Writer - (S - K) if S > K = -MAX(S-K, 0) 0 if S < K = MIN(K-S, 0) Profit to Call Writer Payoff + Option Premium Profit = MIN(K-S, 0) + C Options are what is called a “zero sum game” meaning the profit to the holder is mirrored by the loss to the writer. The payoff to a call writer is exactly the negative of the payoff to the holder. You may remember from algebra that minus the maximum of S minus K or zero equals the minimum of K minus S or zero. For a call writer the BEST case is to sell the call and never hear from it again! In that case, the writer gains the call premium. The payoff and profit for a call writer can be negative. We’ll see the payoffs to both the holder and writer graphically on the next slides. 22

Call Option Payoffs 23

Call Option Profits 24

Payoff & Profit Profiles for Calls
Call Holder The dashed line is the payoff to the call holder. The solid line is the profit to the holder. The distance between the zero line (x-axis) and this line is the call premium. The dotted line is the profit to the call writer. Notice that it is exactly the reflection of the profit to the holder. Also, notice that the call holder’s downside risk is bounded at the call premium price, but the holder’s gain is theoretically unlimited as the stock price rises. The exact opposite is true for the call writer. His profit is bounded at the call premium but his downside risk is unlimited. Call Writer Stock Price 25

Option Payoffs and Profits Put Holder
Payoffs to Put Holder 0 if S > K (K - S) if S < K Profit to Put Holder Payoff - Option Premium Profit = MAX(K-S, 0) - P = MAX(K-S, 0) It would seem that the payoff to puts would be the opposite of calls, but that isn’t the case. The payoff to a put holder is again bounded on the lower end by zero and on the upper end by the strike price. Since the stock price, “S”, cannot drop below zero, K minus S cannot be more than K, the strike price. Again, the profit must be reduced by the premium paid for the option. 26

Option Payoffs and Profits Put Writer
Payoffs to Put Writer 0 if S > K = -MAX(K-S, 0) -(K - S) if S < K = MIN(S-K, 0) Profits to Put Writer Payoff + Option Premium Profit = MIN(S-K, 0) + P As with the call, the payoff to the put writer is the exact negative mirror of the holder’s. As with the writer if a call, a put writer wants to sell the put and never hear from it again, pocketing the option premium. That is the best case for him Let’s look at these payoffs graphically on the next slide. 27

Put Option Payoffs 28

Put Option Profits 29

Payoff & Profit Profiles for Puts
Profits Put Writer The put holder’s loss is bounded by the premium paid. Theoretically, the put holder’s payoff is bounded on the upper end by the strike price since the stock price will not go below zero. Again, the put writer’s payoff is bounded on the upper end by the option premium. Put Holder Stock Price 30

Option Payoffs and Profits
CALL PUT Holder: Payoff MAX(S-K,0) MAX(K-S,0) (Long) Profit MAX(S-K,0)-C MAX(K-S,0)-P “Bullish” “Bearish” Writer: Payoff MIN(K-S,0) MIN(S-K,0) (Short) Profit MIN(K-S,0)+C MIN(S-K,0)+P “Bearish” “Bullish” This table recaps the payoff and profit fundamentals that we have just reviewed. 31

Stock Index Options Option on a stock market index
Cash settlement procedure Actual delivery of all stocks comprising a stock index = impractical If option expires in the money: Option writer pays option holder the intrinsic value of the option Cash settlement procedure same for calls and puts 32 32

American style European style Stock Index Options
OEX = S&P100 index options European style SPX = S&P500 index options DJX = DJIA index options Stock index options are very popular vehicles for managing broad market risk. The three most popular are the “OEX” which is an option on the S&P100 index, the SPX which is an index on the S&P500 and the DJX which is an option on the Dow. As shown on the slide, note that the three are not exactly the same. The OEX is an American style option meaning it can be exercised at any time before its expiration date. Both the SPX and the DJX are European in style, permitting exercise only at expiration. Stock index options are cash-settled. 33 33

Index Option Trading

Stock Index Options: Example
Suppose you bought 5 October 1500 SPX call option contracts at a quoted price of $4.75. (Price per SPX = 100 x quote) How much did you pay? $4.75 X 5 X 100 = $2,375 If the index is at 1520 at expiration, what would you receive? $100 X ( ) X 5 = $10,000 Here’s an example of investing in a stock index option. The October SPX call option with a strike price of 1500 is quoted at $4.75. You pay 100 times the quoted option price. If you buy 5 contracts you would pay $4.75 times 100 times 5 equalling $2,375. If the index is at 1520 at expiration, you would receive $100 times the difference between the index value and your strike price times the number of contracts you hold. In this example, that comes out to $10,000. 36 36

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

At or Out-of-the-Money
Option “Moneyness” “In-the-money” = an option that would yield a positive payoff if exercised “Out-of-the-money” = an option that would NOT yield a positive payoff if exercised In-the-Money At or Out-of-the-Money Call Option S > K S ≤ K Put Option S < K S ≥ K S = stock price K = exercise price 38 38

Option “Moneyness” “Moneyness” relates to the payoff (or lack of one) if an option were exercised immediately. Suppose you hold a call option on Microsoft with a strike price of $25.00. If the stock is currently selling for $20 per share, then your option is “out-of-the-money” since there is no value in exercising it now. Why would you want to exercise an option to buy shares at $25 when you can buy them in the market for $20? If Microsoft is selling for $25, with the strike price on your call at $25, your option is “at-the-money,” indicating that the strike and market price are the same. If Microsoft rises to $30, your call option is “in-the-money” since the value of exercising it immediately is positive - $30 minus $25. 39 39

Arbitrage, Intrinsic Values 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.

Intrinsic Values and Arbitrage: Calls
Call options with American-style exercise must sell for at least their intrinsic value. Suppose: S = $60; C = $5; K = $50. Instant Arbitrage: Buy the call for $5. Immediately exercise the call, and buy the stock for $50. In the next instant, sell the stock at the market price of $60. Profit = $5 per share American call option price = MAX[S - K, 0] 41 41

Intrinsic Values and Arbitrage: Puts
Put options with American-style exercise must sell for at least their intrinsic value. Suppose: S = $40; P = $5; K = $50. Instant Arbitrage: Buy the put for $5. Buy the stock for $40. Immediately exercise the put, and sell the stock for $50. Profit = $5 per share profit American put option price = MAX[K - S, 0] 42 42

Upper Bound for a Call Option Price
Call option price must be < stock price A call option is selling for $65; the underlying stock is selling for $60. Arbitrage: Sell the call, Buy the stock. Worst case: Option is exercised; you pocket $5. Best case: Stock price < $65 at expiration, you keep all of the $65. 43

Upper Bound for a European Put Option Price
European Put option price must be < strike price Put option with a $50 strike price is selling for $60. Arbitrage: Sell the put, Invest the $60 Worse case: Stock price goes to zero You must pay $50 for the stock But, you have $60 from the sale of the put (plus interest) Best case: Stock price ≥ $50 at expiration Put expires with zero value You keep the entire $60, plus interest 44

The Upper Bound for European Put Option Prices
Risk-free rate = 3 % per quarter. 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? The maximum price for a European put option is the present value of the strike price computed at the risk-free rate.

Option Trading Strategies
Type I: Add an option position to a stock position Helps traders modify their stock risk Example: Covered Calls Type II: Spreads. 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

Option Trading Strategies
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.

Option Strategies Protective put Covered call Straddle
Buy a put option on a stock already owned Protects against a decline in value Covered call Selling a call option on stock already owned Exchanges “upside” potential for current income. Straddle Buying or selling a call and a put with the same exercise price. Buying = long straddle; selling = short straddle. 48 48

Protective Put Limit loss; portfolio insurance
+P +S Limit loss; portfolio insurance Position - long the stock and long the put A protective put is a way to limit the loss on a stock holding providing a type of portfolio insurance. Very simply, you buy the stock and buy a put on the stock. You could employ this strategy if you fear a stock’s price may fall, you don’t want to sell your shares but you would like to limit your downside risk. You can see in the table above that, assuming the strike price on the put is below the current price of the stock, the strike price is your downside bound. We’ll see an example on the next slides. 49 49

Protective Put Profit Profit Stock Protective Put Portfolio S -P 50
This graph show you the payoff pattern for holding the stock alone versus the stock plus a put. Again, the distance between the two lines represents the option premium. As described, the protective put strategy limits your downside loss. S -P 50 50

Protective Put Strategy
Suppose you own 100 shares of Microsoft (MSFT) which you bought at the current price of $25.00. You fear MSFT’s price may drop over the next 3-months but you do not want to sell the stock. Put options on MSFT with a strike price of $24 are available. What will be the payoff if you buy a put contract on MSFT? In our example, we own 100 shares of Microsoft selling at $25 per share. You buy a 3-month put contract on Microsoft with a strike price of $24. We’ll see the outcome on the next slide. 51 51

Protective Put Payoffs
As you can see in the table, if the stock price falls below $24, you exercise your put and sell your shares for $24, limiting your loss. If the price is above $24, then your option expires worthless, but you still own the shares. 52 52

Covered Call Income enhancement; sell discipline
Position - Own the stock and write a call. Another option strategy is a covered call. In this case you sell a call option on a stock you own. Portfolio managers use this strategy to enhance the portfolio’s income as well as to enforce a decision to sell. Deciding when to sell a stock is difficult. A portfolio manager might buy a stock with the idea that if the price rises to a certain point, it’s time to sell. Employing the covered call strategy enforces that sell decision, as we’ll see on the next few slides. 53 53

Covered Call Profit Profit Stock Covered Call Portfolio S -P 54
This graph demonstrates the payoff pattern for holding the stock alone versus the covered call strategy. While generating income in the form of the option premium, the covered call limits upside potential by having the stock called away as the price rises. S -P 54 54

Covered Call Strategy Suppose you own 100 shares of Microsoft (MSFT) which you bought at the current price of $25.00. You expect the price to rise and you decide to sell if the price hits $35 per share. Call options on MSFT with a strike price of $35 are available. You decide to sell a call contract on MSFT. What will be your outcomes at option expiration? Again – you own 100 shares of Microsoft at $25. You have decided that if the price hits $35, its time to sell. To enforce your decision you sell a call contract on Microsoft with a strike price of $35. We’ll see the results on the next slide. 55 55

Covered Call Strategy If Microsoft’s price stays or falls below $35, then you have profited by the amount of the call premium. If the price rises above $35, then the call you wrote will be exercised and you will be obligated to sell your shares for $35 each. 56 56

Option Combinations: Straddle
+ S – C + P Provides payoff if stock rises or falls Put and Call have the same strike price (K) and same expiration. There are a wide variety of option combinations that can be created to take advantage of the unique properties of options. We’ll look at one more strategy called a straddle. With a straddle, you buy or already own the stock. You think the price is going to move, possibly due to some impending announcement, but you don’t know which way it will go. To hedge yourself, you buy a put and sell a call with the same strike price and same expiration date. As you can see in the table above, your worst case payoff is the strike price. We’ll look at an example of this strategy on the next slide. 57 57

Option Combinations: Straddle
Suppose you own stock in a gold-mining company called Bre-X Gold. The stock is currently selling for $100 per share. Accusations have arisen about the validity of Bre-X’s claims of finds in Australia. An announcement is expected within a month. If the company’s claims are true, the stock will increase; if they are not, it will fall dramatically. How can you take advantage of this? Bre-X was a real gold mining company in the 1990’s and this situation actually existed in the market at that time. Beginning as a penny stock, Bre-X reached a high of $ per share on the Toronto Stock Exchange before collapsing in 1997. Accusations arose about the validity of Bre-X’s claims of finds in Australia. Investigators were sent to verify the company’s claims. Had you owned Bre-X stock, you could have employed a straddle to protect yourself from the outcome of the investigation of their claims. We’ll see how on the next slide. 58 58

Option Straddle If you sell a call on Bre-X with a strike price of $100 and simultaneously buy a put with the same strike price, your payoff will be $100 regardless of the news on Bre-X. With Bre-X at $100 a share, you sell a call and buy a put with strike prices of $100. As you can see from the table, regardless of what happened to Bre-X’s stock price, your payoff would be $100 per share. This would, of course be reduced by the net premium paid. 59 59

Put-Call Parity The difference between the call price and the put price equals the difference between the stock price and the discounted strike price. Most fundamental relationship in option pricing Generally used for European-style options 60

The Put-Call Parity Formula
Where: C = Call option price today S = Stock price today r = Risk-free interest rate P = Put option price today K = Strike price of the put and the call T = Time remaining until option expiration in years Note: this formula can be rearranged: 61

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. An investor forms the following portfolio: Buy 100 shares of Microsoft stock Write one Microsoft call option contract Buy one Microsoft put option contract. At option expiration, this portfolio will be worth: 62

Put Call Parity Disequilibrium Example
S = K = 105 r = 10.25% C = P = T = 0.5 yrs C = P + S - K / (1 + r)T 17 = (105/1.05) 17  15  Call is overpriced at 17 (should be 15) (or Put is underpriced) One use of the parity relationship permits us to find if an option is fairly valued. In the example above we have a stock selling for $110. We also have two options on this stock – a put and a call – both with a strike price of $105, and both expiring in 6 months. If the call is selling for $17 and the put for $5, with a risk-free rate of 10.25%, are these options correctly priced? Using the Put-Call Parity equation, we solve it for the price of the call, then substitute our values and find that equality doesn’t hold. Either the call is overpriced or the put is underpriced. On the next slide, we’ll see how to take advantage of this discrepancy. 63

Put-Call Parity Arbitrage
C = P S - K/(1+r)T Overpriced Underpriced -C P S PV(X) Sell the call Buy the put Buy the stock “sell the bond” borrow at r We found the call to be overpriced, so we sell (short) it, buy the underpriced put and buy the stock. To complete the equation, we should borrow the discounted value of the strike price at the risk free rate. 64

Synthetic Options C = P + S - K / (1 + r)T -S = + P - C - K/(1+r)T
Sell the stock = Buy Put Sell call Sell bond ( borrow at r) Synthetic Replicate Another use of the Put-Call Parity relationship allows us to create synthetic positions. If a negative means “sell” and a positive means “buy”, we can solve the equation for the position we wish to simulate. In the example above, we want to simulate shorting a stock. The equivalent position in options is to buy a put, sell a call and borrow at the risk-free rate. Note the solid and dotted lines. Synthesizing (without using the risk-free asset) will result in a payoff pattern that graphs exactly the same as shorting the stock but not at the same dollar amounts. Replicating – including the risk-free asset- will result in exactly the same payoff pattern and dollar amounts as shorting the stock. 65

Put-Call Parity with Dividends
(15.4) Where “Div” = the present value of the dividend to be paid before the option expires. The Put-Call Parity equation we have worked with so far assumes no dividends are paid during the life of the option. Equation 15.4 above includes a provision for dividends paid by the underlying stock during the option period. Note that “Div” means the discounted value of the upcoming dividend as shown in the modified equation on the slide. Where dy = dividend yield on the underlying stock 66

Implied Option Prices Suppose a stock is currently selling for $25.
A call option with a strike price of $30 maturing in 6 months is priced at $3.00. The stock will pay a dividend of $1.00 in 3 months. The risk-free rate is 5%. What is the implied price for a 6-month put with a strike price of $30? We have a stock selling for $25. A call option with a strike price of $30 maturing in 6 months is priced at $3.00. The risk-free rate is 5%. If the stock is expected to pay a dividend of one dollar in 3 months, what is the implied price of a 6-month put with a $30 strike price? We’ll work this out on the next slide. 67

Implied Option Price S = $25 K = $30 Div = $1.00
C = $3.00 rf = 5% TD = 3 months = .25 T = 6 months = .5 yrs Substituting into our equation, we find that the implied put price is $8.26. 68

Why Options? “Why buy stock options instead of shares in the underlying stock?” Compare possible outcomes from these two investment strategies: Buy the underlying stock Buy options on the underlying stock 69

Buying the Underlying Stock vs. Buying a Call Option
IBM = $90 per share Call options = $5 per share w/$90 strike price Investment for 100 shares: IBM Shares: $9,000 One call option contract: $500 When the option expires in three months, the price of IBM shares will be: $100, $80, or $90. 70

Example: Buying the Underlying Stock versus Buying a Call Option, Cont.
Buy 100 IBM Shares $9,000 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% 71

Why Options? Conclusion
Call options offer an alternative means of formulating investment strategies: With call options: Lower dollar loss potential Lower dollar gain potential Higher positive percentage return Lower negative percentage return Insider trading venue 72

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:

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