Investments, tenth edition

   Call Options 

 Recall that a call option gives the right to purchase a security at the exercise price. Suppose 

you hold a call option on FinCorp stock with an exercise price of $100, and FinCorp is now 

selling at $110. You can exercise your option to purchase the stock at $100 and simultane-

ously sell the shares at the market price of $110, clearing $10 per share. Yet if the shares 

sell below $100, you can sit on the option and do nothing, realizing no further gain or loss. 

The value of the call option at expiration equals   

Payoff to call holder

5 b

S

T

2 X if S

T

. X

0

if S

T

# X

  

 where   S  

 T 

  is the value of the stock at expiration and  X  is the exercise price. This formula 

emphasizes the option property because the payoff cannot be negative. The option is exer-

cised only if  S  

 T 

  exceeds  X.  If  S  

 T 

  is less than  X,  the option expires with zero value. The loss 

to the option holder in this case equals the price originally paid for the option. More gen-

erally, the  profit  to the option holder is the option payoff at expiration minus the original 

purchase price. 

 The value at expiration of the call with exercise price $100 is given by the schedule: 

Stock price:

$90

$100

$110

$120

$130

Option value:

0

0

10

20

30

 For stock prices at or below $100, the option is worthless. Above $100, the option is worth 

the excess of the stock price over $100. The option’s value increases by $1 for each dollar 

increase in the stock price. This relationship can be depicted graphically as in  Figure 20.2 .  

 The solid line in  Figure 20.2  is the value of the call at expiration. The net  profit  to the 

holder of the call equals the gross payoff less the initial investment in the call. Suppose 

the call cost $14. Then the profit to the call holder would be given by the dashed (bottom) 

line of  Figure 20.2 . At option expiration, the investor suffers a loss of $14 if the stock price 

is less than or equal to $100. 

 Profits do not become positive until the stock price at expiration exceeds $114. The break-

even point is $114, because at that price the payoff to the call,  S  

 T 

   2   X   5  $114  2  $100  5  $14, 

equals the initial cost of the call. 

 Conversely, the writer of the call incurs losses if the stock price is high. In that scenario, 

the writer will receive a call and will be obligated to deliver a stock worth  S  

 T 

  for only  X  

dollars:   

Payoff to call writer

5 b

2(S

T

2 X) if S

T

. X

0

if S

T

# X

  

    20.2 

Values of Options at Expiration 

bod61671_ch20_678-721.indd   685

bod61671_ch20_678-721.indd   685

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Final PDF to printer

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P A R T   V I

  Options, Futures, and Other Derivatives

 The call writer, who is exposed to losses 

if the stock price increases, is willing to bear 

this risk in return for the option premium. 

  Figure  20.3  depicts the payoff and profit 

diagrams for the call writer. These are the 

mirror images of the corresponding diagrams 

for call holders. The break-even point for the 

option writer also is $114. The (negative) pay-

off at that point just offsets the premium origi-

nally received when the option was written.