# Derivatives: Options

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1 Derivatives: Options Call Option: The right, but not the obligation, to buy an asset at a specified exercise (or, strike) price on or before a specified date. Put Option: The right, but not the obligation, to sell an asset at a specified exercise (or, strike) price on or before a specified date. Exercise or Strike Price: Price set for calling (buying) or putting (selling) an asset. Premium: The purchase price of an option. In the money: An option where exercise would be profitable Out of the money: An option where exercise would not be profitable American Option: The buyer of an option has the right to buy (call) or sell (put) the underlying asset on or before the expiration date. European Option: The buyer of an option has the right to buy (call) or sell (put) the underlying asset only on the expiration date. Expiration Date: Normally the third Friday of the month in the United States. Writer of Option: The seller of the option (e.g., write a call means to sell a call option to someone) Stock Option Contract: normally (U.S. exchanges) the right to buy or sell 100 shares

2 Notation S = the value of the asset at the expiration date X = the exercise (strike) price C = the premium (or, price) of the call option P = the premium (or, price) of the put option Payoffs and Profit of Call Options: Payoff = S X if S > X; otherwise 0 Profit = S X C if S > X; otherwise -C Payoffs and Profit of Put Options: Payoff = X S if X > S; otherwise 0 Profit = X S - P if X > S; otherwise -P

3 Simple Numerical Examples of Call and Put Options (1) Call Option Current price of stock \$50 Exercise (strike) price (X) = \$55 Price at expiration (S) = \$60 Premium (C) = \$2 Payoff = S X = \$60 - \$55 = \$5 Profit = S X C = \$60 - \$55 - \$2 = \$3 (2) Put Option Current price of stock \$50 Exercise (strike) price (X) = \$45 Price at expiration (S) = \$40 Premium (P) = \$2 Payoff = X - S = \$45 - \$40 = \$5 Profit = X - S P = \$45 - \$40 - \$2 = \$3

4 Graphical Representation of the Profit on the Call Option Profit/Loss S -2

5 Profit on the Call Option vs. Purchase and Sale of Stock Profit/Loss S -2 Why buy the call? Why not just purchase the stock then sell it when the price goes up?

6 Rate of Return from buying 100 shares of the stock at a price of \$50 then selling all at a price of \$60 Investment = \$50 x 100 = \$5,000 Payoff = \$60 x 100 = \$6,000 Profit = \$10 x 100 = \$1,000 = \$6,000 - \$5,000 \$1,000 Rate of Return = =.20 = 20% \$5,000 Rate of Return from buying a call option contract (100 shares) with a premium of \$2 per share Investment = \$2 x 100 = \$200 Payoff = \$5 x 100 = \$500 = (\$60 - \$55) x 100 Profit = \$3 x 100 = \$300 = (\$60 - \$55 - \$2) x 100 \$300 Rate of Return = = 1.50 = 150% \$200 Suppose you had used all of your \$5,000 to buy call options Investment = \$2 x 2,500 = \$5,000 Payoff = \$5 x 2,500 = \$12,500 Profit = \$3 x 2,500 = \$7,500 \$7,500 Rate of Return = = 1.50 = 150% \$5,000

7 Graphical Representation of the Profit on the Put Option Exercise price (X) = \$45; Price at expiration (S) = \$40; Premium (P) = \$2 Profit/Loss S -2 What about the writer (seller) of the call option and put option?

8 Profit from a Writing a Naked Call Option Exercise (strike) price (X) = \$55; Price at expiration (S) = \$60; Premium (C) = \$2 Profit/Loss +2 0 S

9 Profit from a Writing a Covered Call Option Current Price = 50; Exercise (strike) price (X) = \$55; Price at expiration (S) = \$60; Premium (C) = \$2 First, purchase the stock Profit/Loss S

10 Second, write the call Profit/Loss +2 0 S

11 Profit on the covered call Profit/Loss Buying the stock +7 Buying stock and writing a call option +2 0 S = -48

12 Profit/Loss Profit for the Writer of the Put Option Exercise price (X) = \$45; Price at expiration (S) = \$40; Premium (C) = \$ S -3

13 Option Strategies: Protective Put Action: Purchase Stock and buy a Put Option Assumptions: Purchase price of stock = \$30 Exercise Price = \$30 Premium on Put Option = \$2 Graph the profit potential

14 Option Strategies: Protective Put Profit/Loss Stock Purchase Protective Put S Compare this to the purchase of a stock and writing a call.

15 Option Strategies: Straddle Action: Purchase a call and put Assumptions: Exercise price (X) for both = \$30 Expiration date is the same for both Call option premium = \$3 Put option premium = \$2. Graph the profit potential

16 Option Strategies: Straddle Profit/Loss S

17 Option Strategies: Collar Action: Owning a share, buying a put, and writing a call Assumptions: Current price = \$40 Exercise Price of Call = \$50 Exercise Price of Put = \$30 Premium of Call = Premium on Put (write the call in order to purchase the put) Graph the potential profit

18 Option Strategies: Collar Profit/Loss S

19 Review Problems 1. Suppose the current price of ABC stock is \$30. A call option is selling for \$2 with an exercise price of \$30 set to expire in 3 months. Illustrate the possible profit/loss from purchasing the stock, then selling it in 3 months. On the same graph, illustrate the possible profit/loss from purchasing the call option. 2. Suppose the current price of ABC stock is \$30. You write a call option for a price of \$2 with an exercise price of \$30. Assuming that you do not own the stock illustrate your possible profit/loss from writing the option. 3. Suppose the current price of ABC stock is \$30. After purchasing the stock, you write a call option for a price of \$2 with an exercise price of \$30. Illustrate your possible profit/loss from writing the option. 4. Suppose the current price of XYZ stock is \$70. You do not own the stock, however, you believe that the stock price will be lower in 3 months time. You purchase a put option at a cost of \$5 with an exercise price of \$65. Illustrate your possible profit/loss from the purchase of the put option. 5. The current price of a stock is \$80. Explain and graphically illustrate the potential profits and losses for each of the following investment strategies: a. An investor purchases a call option for \$10 with a strike price of \$85. b. An investor purchases the stock at the current price of \$80 and buys a put option for \$10 with a strike price of \$80. c. An investor purchases the stock at the current price of \$80 and writes (i.e., sells) a call option for \$10 with a strike price of \$80. Under what set of investor beliefs about the movement of the stock price would (c) be a better investment strategy than (b)? 6. An investor purchases a call option and a put option for \$3 each. Explain and graphically illustrate the potential profits and losses for each of the following scenarios: a. The exercise (strike) price for each option is exactly the same --- e.g., \$75. b. The exercise price for the call option exceeds that of the put option --- e.g., X call = \$75 X put = \$65

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