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