OPTIONS MARKETS AND VALUATIONS (CHAPTERS 16 & 17)

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1 OPTIONS MARKETS AND VALUATIONS (CHAPTERS 16 & 17) WHAT ARE OPTIONS? Derivative securities whose values are derived from the values of the underlying securities. Stock options quotations from WSJ. A call option buyer has the right to buy, but not the obligation to buy, a certain quantity of the underlying asset at a predetermined (strike or exercise) price on or before the expiration date. The seller (writer) of a call option agrees to sell a certain quantity of the underlying asset at the strike price to the call option buyer on or before the expiration date if the buyer chooses to exercise the option. A put option buyer has the right to sell, but not the obligation to sell, a certain quantity of the underlying asset at the strike price on or before the expiration date. The seller (writer) of a put option agrees to buy a certain quantity of the underlying asset at the strike price from the put option buyer on or before the expiration date if the buyer chooses to exercise the option. The buyer pays an option premium (call or put price) to the seller. 16-1

2 BASIC FEATURES OF AN OPTION CONTRACT 1. Identity of the underlying security Individual common stock; stock and bond market indexes; foreign currencies; futures contracts; Treasury bills and bonds 2. Strike or exercise price 3. Expiration or maturity date Short-term: stock options usually expire in less than 9 months LEAPS (Long-Term Equity Anticipation Shares) are options on certain stocks and stock indexes that have expirations of up to three years The actual expiration day of a stock and index option is the third Friday of the month 4. Contract size One stock option contract represents rights to 100 shares of the underlying stock Options on indexes are specified as a multiple, usually 100; e.g., OEX (S&P 100) 5. Exercise style European options can be exercised only on the exercise date; most index options American options can be exercised at any time on or before the exercise date; most individual stock options 6. Delivery or settlement procedure 16-2

3 OPTION TRADING Option exchanges: CBOE; New York; American; Philadelphia; Pacific Option Clearing Corporation Stock Orders vs. Options Orders Stock orders < Buy! sell < Sell short! buy to cover Options order < Buy Open (call or put) Then three possible actions: 1. Sell Close (offset order) 2. Exercise the option 3. Let the option expire < Sell Open (Call or Put) Then three possible outcomes: 1. Buy Close (offset order) 2. The buyer exercises the option 3. Nothing (the buyer chooses to let the option expire) 16-3

4 At-the-Money option: when strike price = current stock price In-the-Money Call option: when strike price < current stock price Put option: when strike price > current stock price Out-of-the-Money Call option: when strike price > current stock price Put option: when strike price < current stock price Option Price (Premium): The price the buyer of an option (call or put) pays the seller of the option Intrinsic value for in the money call = S 0 - X Intrinsic value for in the money put = X - S 0 Premium (price) = intrinsic value + speculative premium Early Exercise of Options 16-4

5 BASIC OPTIONS STRATEGIES Buying stocks vs. buying call options Selling (writing) naked (or uncovered) call options Short selling stocks vs. buying put options Selling put options ADVANCED OPTIONS STRATEGIES Covered calls (buy stock and sell call) Protective puts (buy stock and buy put) BUYING STOCKS VS. BUYING CALL OPTIONS Buy Stock Pay $20 per share Profit/loss table $0 $10 $30 $40 Profit/Loss In dollars Profit/Loss In % -100% -50% 50% 100% º Unlimited potential profit but limited potential loss Profit/loss diagram 16-5

6 Buy Call Strike price, X = $20; current stock price, S 0 = $20 Pay call premium $2 or $200 per contract = stock price at expiration Call value at expiration = ( - X) if ( > X) = 0 if ( # X) Profit/loss table Call Value Call Premium Profit/Loss Return (%) $ % $ % $ % $ % $ % º Unlimited potential profit but limited potential loss (the call premium) º Buying a call option provides a much greater leverage than buying the stock itself and also a limited dollar risk Profit/loss diagram 16-6

7 SELL NAKED OR UNCOVERED CALL Sell call option and receive call premium $2 or $200 per contract The seller does not own the underlying stock Strike price, X = $20; current stock price, S 0 = $20 Call value at expiration = -( - X) if ( > X) = 0 if ( # X) Profit/loss table Call Value Call Premium Profit/Loss $ $ $ $ $ º Limited potential profit (the call premium) but unlimited potential loss Profit/loss diagram 16-7

8 SHORT SELLING STOCKS VS. BUYING PUT OPTIONS Short Sell Stock Short sell at $20 per share Profit/loss table $0 $10 $30 $40 Profit/Loss In dollars Profit/Loss In % 100% 50% -50% -100% º Limited potential profit but unlimited potential loss Profit/loss diagram 16-8

9 Buy Put Strike price, X = $20; current stock price, S 0 = $20 Pay put premium $1 or $100 per contract The buyer does not own the underlying stock Put value at expiration = 0 if ( $ X) = (X - ) if ( < X) Profit/loss table Put Value Put Premium Profit/Loss $ $ $ $ $ º Limited, but large, potential profit and limited loss (the put premium) Profit/loss diagram 16-9

10 SELL PUT Strike price, X = $20; current stock price, S 0 = $20 Receive put premium $1 or $100 per contract Put value at expiration = 0 if ( $ X) = -(X - ) if ( < X) Profit/loss table Put Value Put Premium Profit/Loss $ $ $ $ $ º Limited potential profit and limited, but large potential loss Profit/loss diagram 16-10

11 COVERED CALL The call option seller (or writer) owns the underlying stock Strike price, X = $40; current stock price, S 0 = $38 Receive call premium $4 or $400 per contract Profit/loss table ) Stock Value Call Value Call Premium Profit/Loss $ $ $ $ $ º The call premium acts like a cushion or hedge when stock price drops º Limited potential profit and limited, but large, potential loss º Risk reducing strategy Profit/loss diagram 16-11

12 PROTECTIVE PUT The buyer of the put options owns the underlying stock, similar to buying insurance or forming a hedge against a decline in stock price Strike price, X = $20; current stock price, S 0 = $22 Pay put premium $2 or $200 per contract Profit/loss table ) Stock Value Put Value Put Premium Profit/ Loss $ $ $ $ $ º Unlimited potential profit but limited loss º The loss = the put premium or insurance premium when X = S 0 Profit/loss diagram 16-12

13 VALUATION OF CALL AND PUT OPTIONS Determinants of Option Values (Chapter 17, P. 542) Call Option Put Option Current Stock Price + - Exercise Price - + Time to Expiration + + Stock Volatility + + Interest Rate

14 The Put-Call Parity (equation 17.2) Portfolio A: Buy a call option and sell a put option on the same stock with the same exercise price and expiration date < The cost of investing in Portfolio A = C - P < The payoff Payoff at Expiration Position < X > X Buy call 0 - X Sell put -(X - ) 0 Total - X - X Portfolio B: Buy the stock (paying S 0 ) and borrowing a loan with a value = the present value of the exercise price or X/(1 + r F ) T < The cost of investing in Portfolio B = S 0 - X/(1 + r F ) T < The payoff Payoff at Expiration Position < X > X Buy stock Borrow loan -X -X Total - X - X Both portfolios have the same payoffs º both must have the same costs C - P = S 0 - X/(1 + r F ) T Arbitrage opportunity exists if the parity is violated 16-14

15 Arbitrage Example Example 17.2 Stock S 0 = $110 Call option (X = $105, 6-month expiration) C = $17 Put option (X = $105, 6-month expiration) P = $5 Risk free interest rate r F = 10.25% Portfolio A: C - P = $12 Portfolio B: S 0 - X/(1 + r F ) T = /(1.1025) 0.5 = = $10 Portfolio A is overvalued and/or Portfolio B is undervalued Arbitrage strategy: Sell Portfolio A and buy Portfolio B Payoff table Payoff at expiration Position Immediate Cash Flow = $0 = $200 Sell call (X = $105) $17 $0 -$95 Buy put (X = $105) -$5 $105 $0 Buy stock -$110 $0 $200 Borrow loan $100 -$105 -$105 Total $2 $0 $0 HOMEWORK: CHAPTER 16: 1, 2, 3, 4, 5(no diagram), 20(A&B) and CK 1 CHAPTER 17: 2(A-D) 16-15

16 SOLUTIONS: CHAPTER Answer c is false (why) 2. Answer c (why) 3. $ Option Premium Option Value Profit/Loss A Call X = B Put X = C Call X = D Put X = E Call X = F Put X = Investment Value: Stock price $80 $100 $110 $120 All stocks (100 shares) 8,000 10,000 11,000 12,000 All options (10 contracts) ,000 20,000 Bills + options 9,360 9,360 10,360 11,360 Rate of returns: All stocks (100 shares) -20% 0% 10% 20% All options (10 contracts) -100% -100% 0% 100% Bills + options -6.4% -6.4% 3.6% 13.6% 16-16

17 20. (A) (B) Sally does better when the stock price is high, but worse when the stock price is low. SOLUTIONS: CHAPTER (A) Put A (B) Put B (C) Call B (D) Call B 16-17

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