Introduction to Corporate Finance

8: Options

the money, the seller earns an $8 profit. If the option expires in the money, the seller may realise a net

profit or a net loss, depending on how high the share price is at that time. Whereas the call option buyer

enjoys the potential for unlimited gains, the option seller faces exposure to the risk of unlimited losses.

Rationally, if $8 is sufficient to induce someone to sell this option and thereby face the potential of huge

losses, it must be the case that the seller perceives the probability of a large loss to be relatively low.

8-2b PuT OPTION PaYOFFS

Figure 8.2 shows payoffs for put option buyers (long) and sellers (short). We maintain the assumption that

the strike price equals $75, but, in this figure, the option premium is $7. For an investor holding a put option,

the payoff rises as the share price falls below the option’s strike price. However, unlike a call option, a put

option’s potential gains are limited by a share price that cannot fall below zero (because the law provides

limited liability for a company’s shareholders). The maximum gain on this particular put equals $75 (or $68 on

a net basis after subtracting the premium), whereas the maximum loss is the $7 option premium.

LO8.2

FIGure 8.2 PAYOFF OF A PUT OPTION WITH X = $75

The top graph illustrates, from the option buyer’s perspective,

how a put option’s payoff varies as the underlying share price

changes. The red line shows that the put option will be worthless

on the expiration date if the share price is $75 or higher. The

buyer’s payoff rises dollar for dollar as the share price drops

below $75. The blue line illustrates the put option’s net payoff,

which takes into account the $7 premium that the buyer paid to

acquire the option. The buyer’s breakeven point occurs when the

share price is $68 ($75 − $7). At lower share prices, the buyer

makes a profit, and at higher prices, the buyer loses money. The

buyer’s maximum profit is $68, and the maximum loss is $7.

The lower graph illustrates the seller’s perspective. The red line

shows that the put option’s payoff is $0 if the share price is $75

or higher, but the seller loses money as the share price falls

below $75. The blue line illustrates the net payoff and reflects the

$7 premium that the seller received from the buyer. The seller’s

breakeven point is $68. At higher share prices, the seller makes

a net profit, and at lower prices the seller loses money. The

seller’s maximum profit is $7, and the maximum loss is $68.

7

Put payoff ($)

Share price on expiration date ($)

25 50 75 100 125 150

68

0

–25

–50

–75

–68

Payoff to sellers

Payoff

Net payoff

Share price on expiration date ($)

100

150

125

25 50

68

Put payoff ($)

0

25

50

75

68

option premium

Payoff to buyers

–7

Payoff

Net payoff

75

option premium