Options
Options
Put Options
? Call Options
? Examples of derivatives
?
Peter O’Grady
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Put Options
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Put Options
Define S as the price of the underlying
asset, and K as the strike price.
? In, out of, and at the money for puts
?
A put option is a contract that gives the
owner the right, but not the obligation, to
sell an underlying asset, at a fixed price
($K), on (or on or before) a specific day.
? The put writer is obligated to buy the
underlying asset, and pay $K for it.
?
– In the money if S < K
– Out of the money if S > K
– At the money if S ~ K
– Deep in (out of) the money if S << K
(S >> K)
?
Intrinsic value of a put = max(0,K-S)
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Profit Diagram -- Long Put
(Buying a Put)
Value of Put at Expiration (A.K.A.
Payoff Diagram)
PT
Profit
0
0
K
ST
Just lower the payoff diagram
by the put premium (price of
put)to get the profit diagram
K
ST
put premium
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Example of a Put Option
?
Example of a Put Option (cont.)
buy a put option to purchase 100 Exxon shares
Profit ($)
– strike price = $70
– price of an option to buy one share = $7
?
?
3000
2500
2000
initial investment is 100 x $7 = $700
The outcome
1500
Terminal stock price ($)
1000
500
– Exxon’ s share price is $55 at the expiration
– to exercise the option for a gain of
0
40
50
60
70
80
90
100
-700
-1000
($70-$55) x 100 = $1,500
– the net gain = $1,500 - $700 = $800
-1500
Figure Profit from buying a Put Option on 100 Exxon share. Option
price = $7; strike price = $70
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Profit Diagram – Short Put
(Selling a Put)
Insurance
?
Profit
0
K
8
ST
Insurance. If you own the underlying
asset, buying a put provides
protection against the possibility that
the underlying asset price will fall
below $K. Of course, insurance costs
money (the put premium).
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Call Options
Call Options
A call option is a contract that gives the
owner the right, but not the obligation, to
buy an underlying asset, at a fixed
price, on (or on or before) a specific
day.
? The fixed price is called the strike price,
or the exercise price.
?
?
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In, out of, and at the money: Define S
as the price of the underlying asset, and
K as the strike price. Then, for a call:
– In the money if S > K
– Out of the money if S < K
– At the money if S ~ K
– Deep in (out of) the money if S >> K
(S << K)
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Profit Diagram -- Long Call
(Buying a Call Option)
Value of Call at Expiration, (A.K.A.
Payoff Diagram)
CT
Just lower the payoff diagram
by the call premium (price of the option), to get the
profit diagram
Profit
call premium
0
K
K
ST
0
ST
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Example of a Call Option
?
Example of a Call Option (cont.)
buy a call option to purchase 100 MSFT share
– strike price = $52
– current share price = $50
?
?
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Profit ($)
1200
1000
– price of an option to buy one share = $2
initial investment is 100 x $2 = $200
800
600
400
The outcome
– MSFT’ s share price is $55 at the expiration
Terminal stock price ($)
200
0
50
60
70
80
90
-200
– to exercise the option for a gain of ($55-$52) x 100
= $300
– the net gain = $300 - $200 = $100
-400
-600
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Example of a Call Option
?
Example of a Call Option (cont.)
buy a call option to purchase 100 IBM shares
– strike price = $100
– current share price = $98
?
?
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Profit ($)
3000
2500
– price of an option to buy one share = $5
initial investment is 100 x $5 = $500 (Worse case is
that this will be lost)
The outcome
2000
1500
1000
Terminal stock price ($)
500
0
– IBM ’s share price is $115 at the expiration
– to exercise the option for a gain of
90
100
110
120
130
-500
-1000
-1500
($115-$100) x 100 = $1,500
– the net gain = $1,500 - $500 = $1,000
Figure Profit from buying a Call Option on 100 IBM share. Option
price = $5; strike price = $100
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Profit Diagram – Short Call
(Selling a Call Option)
Example of a Call Option (cont.)
Profit ($)
1000
Profit
500
0
Terminal stock price ($)
90
-500
100
110
120
130
-1000
-1500
0
-2000
ST
K
-2500
-3000
-3500
Figure Profit from writing a Call Option on 100 IBM share. Option
price = $5; strike price = $100
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Example of a Put Option (cont.)
Profit ($)
700
0
-500
40
Option Positions (cont.)
60
70
80
90
Profit
Profit
Terminal stock price ($)
50
20
X
100
X
-1000
ST
ST
(a) long call
-1500
-2000
Profit
Profit
-2500
(b) short call
-3000
-3500
-4000
X
Figure Profit from writing a Put Option on 100 Exxon share. Option
price = $7; strike price = $70
ST
(c) long put
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X
ST
(d) short put
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