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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.

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Stock Options

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  1. 15 Stock Options

  2. 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

  3. Put and Call Options • Call 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. 3

  4. 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 4

  5. Listed Option Quotationswww.wsj.com

  6. Option Price Quotes • Option Chain: • 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

  7. Stock Option Ticker Symbol and Strike Price Codes 7

  8. Listed Option Quotes on the Web 8

  9. 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

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

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

  12. Option Price QuotesCalls 12

  13. Option Price QuotesPuts 13

  14. Option Price Quotes 14

  15. 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: www.optionsclearing.com. 15

  16. 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.

  17. 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

  18. Option Exercise • American-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

  19. 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 19

  20. 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

  21. Option Payoffs & ProfitsCall 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) 21

  22. Option Payoffs & ProfitsCall 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 22

  23. Call Option Payoffs 23

  24. Call Option Profits 24

  25. Payoff & Profit Profiles for Calls Payoff Profit Call Holder 0 Call Writer Stock Price 25

  26. 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) 26

  27. 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 27

  28. Put Option Payoffs 28

  29. Put Option Profits 29

  30. Payoff & Profit Profiles for Puts Profits Put Writer 0 Put Holder Stock Price 30

  31. 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” 31

  32. 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

  33. Stock Index Options American style OEX = S&P100 index options European style SPX = S&P500 index options DJX = DJIA index options 33

  34. Index Option Trading

  35. Index Option Trading

  36. 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 (1520-1500) X 5 = $10,000 36

  37. 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.

  38. 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 S = stock price K = exercise price 38

  39. Option “Moneyness” 39

  40. Arbitrage, Intrinsic Values and Option Pricing Bounds • Arbitrage: • 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.

  41. 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

  42. 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. Buythe 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

  43. 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

  44. 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

  45. The Upper Bound for European Put OptionPrices • 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.

  46. 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

  47. 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.

  48. Option Strategies Protective put 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

  49. Protective Put +P +S Limit loss; portfolio insurance Position - long the stock and long the put 49

  50. Protective Put Profit Profit Stock Protective Put Portfolio S -P 50

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