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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 further the underlying asset falls in
value. Because of this negative relationship with the underlying asset, puts can be good hedging
instruments 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 instrument depicted is not an option.
The payoff diagram for a written put option position is the mirror image of the purchased put‟s
payoff diagram. Such a payoff diagram is shown in Exhibit 15.4. The possible payoff reaped by the
buyer of the put option is exactly equal to the possible outflow 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 that of a short call option. Similarly, notice that a long call option
payoff is not the same as that of 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 flows. Long calls and long puts have to be paid for up front, and
then receive a subsequent positive payoff depending on what happens to the underlying stock. Short
calls and short puts receive all of their cash inflows up front and then become potential liabilities.
Exhibit 15.4 Payoff diagram for a written put option position.