Buying Put Options The buying of a put option creates a financial position referred to as a

Buying Put Options The buying of a put option creates a financial position referred to as a

long put position. To illustrate this position, we assume a hypothetical put option on one unit of Asset X with one month to maturity and an exercise price of $100. Assume the put option is selling for $3 and the price of Asset X at the expiration date is $60. The profit or loss for this position at the expiration date depends on the market price of Asset X. The possible outcomes are:

FOUNDATIONS

EXHIBIT 4.3 Profits and Losses on the Writing of a Call Option that Allows the Call

Option Buyer to Buy the Stock at $60. The Call Writer Receives $2 for this Option.

1. If Asset X’s price is greater than $60, the buyer of the put option will not exercise it because exercising would mean selling Asset X to the writer for a price that is less than the market price. A loss of $3 (the option price) will result in this case from buying the put option. Once again, the option price represents the maximum loss to which the buyer of the put option is exposed.

2. If the price of Asset X at expiration is equal to $60, the put will not

be exercised, leaving the put buyer with a loss equal to the option price of $3.

3. Any price for Asset X that is less than $60 but greater than $57 will result in a loss; exercising the put option, however, limits the loss to less than the option price of $1. For example, suppose that the price is $59 at the expiration date. By exercising the option, the option buyer will realize a loss of $2. This is because the buyer of the put option can sell Asset X, purchased in the market for $59, to the writer for $60, realizing a gain of $1. Deducting the $3 cost of the option results in a loss of $2.

4. At a $57 price for Asset X at the expiration date, the put buyer will break even. The investor will realize a gain of $3 by selling Asset X to the writer of the option for $60, offsetting the cost of the option ($3).

5. If Asset X’s price is below $57 at the expiration date, the long put position (the put buyer) will realize a profit. For example, suppose the price falls at expiration to $46. The long put position will produce a profit of $11: a gain of $14 for exercising the put option less the $3 option price.

Introduction to Derivatives

EXHIBIT 4.4 Profits and Losses on the Exercise of a Put Option to Sell the Stock at

$60. The Investor Pays $2 for this Put Option.

The profit and loss profile for the long put position is shown in graphical form in Exhibit 4.4. As with all long option positions, the loss is limited to the option price. The profit potential, however, is substan- tial: The theoretical maximum profit is generated if Asset X’s price falls to zero. Contrast this profit potential with that of the buyer of a call option. The theoretical maximum profit for a call buyer cannot be determined beforehand because it depends on the highest price that can

be reached by Asset X before or at the option expiration date. Writing (Selling) Put Options

Writing a put option creates a position referred to as a short put position. The profit and loss profile for a short put option is the mirror image of the long put option. The maximum profit from this position is the option price. The theoretical maximum loss can be substantial should the price of the underlying fall; at the extreme, if the price were to fall all the way to zero, the loss would be as large as the exercise price less the option price. Exhibit 4.5 graphically depicts this profit and loss profile.

To summarize, buying calls or selling puts allows the investor to gain if the price of the underlying rises. Selling calls and buying puts allows the investor to gain if the price of the underlying falls.