446 Planning and Forecasting
price. At that point the put option owner would have the right to sell a worth-
less stock for $100. From that point, the put option payoff falls one dollar for
each dollar that the stock price rises. The payoff reaches zero when the stock
price equals the strike price, and then remains at zero no matter how much
higher the stock price goes. As is the case with call options, the put option can-
not fall in value below zero. Once the put option premium is paid, the owner is
never called upon to make another payment. Any subsequent cash f low is posi-
tive. It is altogether possible, however, for the buyer of the put option to lose
the entire premium, so one should not think that buying a put option is a safe
investment.
Notice that the put option payoff rises as the stock price falls. For this
reason, puts are thought of as “bearish” instruments—instruments that are
more profitable the more the underlying asset falls in value. Because of this
negative relationship with the underlying asset, puts can be good hedging in-
struments for someone who owns the underlying asset.
Like the call option’s payoff diagram, the put’s payoff diagram is
kinked—that is, there is an elbow at the strike price. A kinked payoff diagram
is the hallmark of an option. If a payoff diagram has no kink, then the instru-
ment depicted is not an option.
The payoff diagram for a written put option position is the mirror image
of the put’s payoff diagram. Such a payoff diagram is shown in Exhibit 13.4.
The possible payoff reaped by the buyer of the put option is exactly equal to
the possible outf low paid by the writer. Put options too are a zero-sum game.
Notice that whereas the writer of a call option has unlimited potential liability,
the writer of a put option has a potential liability limited to the strike price.
Furthermore, notice that a long put option payoff looks nothing like a short
call option. Similarly, notice that a long call option payoff is not the same as a
short put. Both long puts and short calls are bearish positions, just as both short
puts and long calls are bullish positions, but each of these four positions is
unique in the direction, size, and timing of cash f lows. Long calls and long puts
EXHIBIT 13.3 Put option payoff diagram.
040
2060801001200 10203040506070 80 90100 110120 130Payoff (dollars)Terminal stock price (Strike price = $100)