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
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
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
Graphical Representation of the Profit on the Call Option
Profit/Loss
0 50 S
55 60 -2
+3
Profit on the Call Option vs. Purchase and Sale of Stock
Profit/Loss
0 50 S
55 60 -2
+3 +10
Why buy the call? Why not just purchase the stock then sell it when the price goes up?
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
Rate of Return = .20 20% 000
, 5
$ 000 , 1
$ = =
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
Rate of Return = 1.50 150% 200
$ 300
$ = =
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
Rate of Return = 1.50 150% 000
, 5
$ 500 , 7
$ = =
Graphical Representation of the Profit on the Put Option
Exercise price (X) = $45; Price at expiration (S) = $40; Premium (P) = $2
Profit/Loss
0 40 S
45 -2
+3
What about the writer (seller) of the call option and put option?
Profit from a Writing a “Naked” Call Option
Exercise (strike) price (X) = $55; Price at expiration (S) = $60; Premium (C) = $2
Profit/Loss0 S
55 60 +2
-3
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
0 50 S
60
Second, write the call…
Profit/Loss
0 S
55 60 +2
-3
Profit on the ‘covered’ call…
Profit/Loss
0 S
55 60 +2
2-50= -48
50 +7
48
Buying the stock
Buying stock and writing a call option
Profit for the Writer of the Put Option
Exercise price (X) = $45; Price at expiration (S) = $40; Premium (C) = $2
Profit/Loss0 40 S
45 -3
+2
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 …
Option Strategies: Protective Put
Profit/Loss
0 30 S
Stock Purchase Protective Put
-2
Compare this to the purchase of a stock and writing a call.
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 …
Option Strategies: Straddle
Profit/Loss
0 S
30
-5 +25
35
25
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…
Option Strategies: Collar
Profit/Loss
0 S
40
-10 +10
50
30
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., Xcall = $75 Xput = $65
