1. OPTIONS MARKETS: INTRODUCTION Derivative Securities Option contracts are written on common stock, stock indexes, foreign exchange, agricultural commodities, precious metals and interest rate futures

2. THE OPTION CONTRACT A call option gives its holder the right to purchase an asset for a specified price, called exercise, or strike price, on or before some specified expiration date. A call option gives its holder the right to purchase an asset for a specified price, called exercise, or strike price, on or before some specified expiration date. A put option gives its holder the right to sell an asset for a specified price, called exercise, or strike price, on or before some specified expiration date. A put option gives its holder the right to sell an asset for a specified price, called exercise, or strike price, on or before some specified expiration date.

3. Example 20.1 Profits and Losses on a Call Option. Example 20.1 Profits and Losses on a Call Option. Value at expiration = Stock price – Exercise price = $23.50 - $22.50 = $1 Despite the $1 payoff at maturity, the investor sell realizes a loss of $.15 on the call because it cost $1.15 to purchase Profit = Final value – Original investment = $1 - $1.15 = -$.15 In the money; describes an option whose exercise would produce profits. Out of the money describes an option where exercise would not be profitable In the money; describes an option whose exercise would produce profits. Out of the money describes an option where exercise would not be profitable

4. American and European Options An American option allows its holder to exercise the right to purchase (if a call) or sell (if a put) the underlying asset on or before the expiration date. European options allow for exercise of the option only on the expiration date.

5. VALUES OF OPTIONS AT EXPIRATION Suppose you hold a call option on IBM stock with an exercise price of $100, and IBM is now selling at $110. You can exercise your option to purchase the stock at $100 and simultaneously sell the shares at the market price of $110, clearing $10 per share. Yet if the shares sell below $100, you can sit on the option and do nothing, realizing no further gain or loss. Suppose you hold a call option on IBM stock with an exercise price of $100, and IBM is now selling at $110. You can exercise your option to purchase the stock at $100 and simultaneously sell the shares at the market price of $110, clearing $10 per share. Yet if the shares sell below $100, you can sit on the option and do nothing, realizing no further gain or loss. Payoff to call holder = S T – X if S T > X Payoff to call holder = S T – X if S T > X 0 if S T ≤ X S T is the value of the stock at expiration X is the exercise price

6. The value at expiration of the call on IBM with exercise price $100 is given by the schedule The value at expiration of the call on IBM with exercise price $100 is given by the schedule IBM value:$90$100$110$120$130 Option value:0 0 10 20 30 Payoff to call writer = - (S T – X) if S T > X Payoff to call writer = - (S T – X) if S T > X 0 if S T ≤ X

7. Call Option Payoffs –20 120 204060 80 100 –40 20 40 60 Stock price ($) Option payoffs ($) Buy a call Exercise price = $50 50

8. Call Option Payoffs –20 120 204060 80 100 –40 20 40 60 Stock price ($) Option payoffs ($) Sell a call Exercise price = $50 50

9. Call Option Profits Exercise price = $50; option premium = $10 Sell a call Buy a call –20 120 204060 80 100 –40 20 40 60 Stock price ($) Option payoffs ($) 50 –10 10

10. Put options If IBM shares were to fall to $90, a put option with exercise price $100 could be exercised to clear $10 for its holder. Payoff to put holder = 0 if S T ≥ X X - S T if S T < X X - S T if S T < X

11. Basic Put Option Pricing Relationships at Expiry At expiry, an American put option is worth the same as a European option with the same characteristics. If the put is in-the-money, it is worth X – S T. If the put is out-of-the-money, it is worthless. P = Max[X – S T, 0]

12. Put Option Payoffs –20 0 204060 80 100 –40 20 0 40 60 Stock price ($) Option payoffs ($) Buy a put Exercise price = $50 50

13. Put Option Payoffs –20 0204060 80 100 –40 20 0 40 –50 Stock price ($) Option payoffs ($) Sell a put Exercise price = $50 50

14. Put Option Profits –20 204060 80 100 –40 20 40 60 Stock price ($) Option payoffs ($) Buy a put Exercise price = $50; option premium = $10 –10 10 Sell a put 50

15. Selling Options Exercise price = $50; option premium = $10 Sell a call Buy a call 50 60 40 100 –40 40 Stock price ($) Option payoffs ($) Buy a put Sell a put The seller (or writer) of an option has an obligation. The purchaser of an option has an option. –10 10 Buy a call Sell a put Buy a put Sell a call

16. Option versus stock investment Why would you purchase a call option rather than buy IBM stock directly? -Strategy A: -Strategy B: -Strategy C:

17. OPTION STRATEGY Protective put; purchase of stock combined with a put option that guarantees minimum proceeds equal to the put’s exercise price Table 20.1 Value of Protective Put Portfolio at Option Expiration S T ≤ X S T > X S T ≤ X S T > X Stock S T S T + Put X - S T 0 + Put X - S T 0 Total X S T Total X S T

18. Protective Put Strategy: Buy a Put and Buy the Underlying Stock: Payoffs at Expiry Buy a put with an exercise price of $50 Buy the stock Protective Put payoffs $50 $0 $50 Value at expiry Value of stock at expiry

19. Protective Put Strategy Profits Buy a put with exercise price of $50 for $10 Buy the stock at $40 $40 Protective Put strategy $40 $0 -$40 $50 Value at expiry Value of stock at expiry -$10

20. Covered call; a combination of selling a call on a stock together with buying the stock Table 20.2 Value of Covered Call Position at Option Expiration S T ≤ X S T > X S T ≤ X S T > X Payoff of stock S T S T Payoff of stock S T S T + Payoff of written call -0 -(S T – X) Total S T X Total S T X

21. Covered Call Strategy Sell a call with exercise price of $50 for $10 Buy the stock at $40 $40 Covered Call strategy $0 -$40 $50 Value at expiry Value of stock at expiry -$30 $10

22. Straddle; a combination of buying both a call and a put on the same asset, each with the same exercise price and expiration date. The purpose is to profit from expected volatility.

23. Long Straddle: Buy a Call and a Put 30 4060 70 30 40 Stock price ($) Option payoffs ($) Buy a put with exercise price of $50 for $10 Buy a call with exercise price of $50 for $10 A Long Straddle only makes money if the stock price moves $20 away from $50. $50 –20

24. Long Straddle: Buy a Call and a Put –30 30 4060 70 –40 Stock price ($) Option payoffs ($) $50 This Short Straddle only loses money if the stock price moves $20 away from $50. Sell a put with exercise price of $50 for $10 Sell a call with an exercise price of $50 for $10 20

25. bond Put-Call Parity: p 0 + S 0 = c 0 + E/(1+ r) T 25 Stock price ($) Option payoffs ($) Consider the payoffs from holding a portfolio consisting of a call with a strike price of $25 and a bond with a future value of $25. Call Portfolio payoff Portfolio value today = c 0 + (1+ r) T E

26. Put-Call Parity: p 0 + S 0 = c 0 + E/(1+ r) T 25 Stock price ($) Option payoffs ($) Consider the payoffs from holding a portfolio consisting of a share of stock and a put with a $25 strike. Portfolio value today = p 0 + S 0 Portfolio payoff

27. Put-Call Parity: p 0 + S 0 = c 0 + E/(1+ r) T Since these portfolios have identical payoffs, they must have the same value today: hence Put-Call Parity: c 0 + E/(1+r) T = p 0 + S 0 25 Stock price ($) Option payoffs ($) 25 Stock price ($) Option payoffs ($) Portfolio value today = p 0 + S 0 Portfolio value today (1+ r) T E = c 0 +

28. Warrants are essentially call options issued by a firm. One important difference between calls and warrants is that exercise of a warrant requires the firm to issue a new share of stock – the total number of shares outstanding increases