Buying Call Options The purchase of a call option creates a position referred to as a long call

Buying Call Options The purchase of a call option creates a position referred to as a long call

position. To illustrate this position, assume that there is a call option on Asset X that expires in one month and has an exercise price of $60. The option price is $2. What is the profit or loss for the investor who pur- chases this call option and holds it to the expiration date?

The profit and loss from the strategy will depend on the price of Asset X at the expiration date. A number of outcomes are possible.

1. If the price of Asset X at the expiration date is less than $60 (the option price), then the investor will not exercise the option. It would be fool- ish to pay the option writer $60 when Asset X can be purchased in the market at a lower price. In this case, the option buyer loses the entire option price of $2. Notice, however, that this is the maximum loss that the option buyer will realize regardless of how low Asset X’s price declines.

2. If Asset X’s price is equal to $60 at the expiration date, there is again no economic value in exercising the option. As in the case where the price is less than $60, the buyer of the call option will lose the entire option price, $2.

3. If Asset X’s price is more than $60 but less than $62 at the expiration date, the option buyer will exercise the option. By exercising, the option buyer can purchase Asset X for $60 (the exercise price) and sell it in the market for the higher price. Suppose, for example, that Asset X’s price is $61 at the expiration date. The buyer of the call option will realize a $1 gain by exercising the option. Of course, the cost of pur- chasing the call option was $2, so $1 is lost on this position. By failing to exercise the option, the investor loses $2 instead of only $1.

4. If Asset X’s price at the expiration date is equal to $62, the investor will exercise the option. In this case, the investor breaks even, realizing a gain of $2 that offsets the cost of the option, $2.

5. If Asset X’s price at the expiration date is more than $62, the investor will exercise the option and realize a profit. For example, if the price is $70, exercising the option will generate a profit on Asset X of $10. Reducing this gain by the cost of the option ($2), the investor will real- ize a net profit from this position of $8.

Exhibit 4.2 shows in graph form the profit and loss for the buyer of the hypothetical call option. While the break-even point and the loss will depend on the option price and the exercise price, the profile shown in Exhibit 4.2 will hold for all buyers of call options. The shape indi- cates that the maximum loss is the option price and that there is sub- stantial upside potential.

Introduction to Derivatives

EXHIBIT 4.2 Profits and Losses on the Exercise of a Call Option to Buy the Stock at

$60. The investor Pays $2 for this Call Option.

Writing (Selling) Call Options The writer of a call option is said to be in a short call position. To illus-

trate the option seller’s (writer’s) position, we use the same call option we used to illustrate buying a call option. The profit and loss profile of the short call position (that is, the position of the call option writer) is the mir- ror image of the profit and loss profile of the long call position (the posi- tion of the call option buyer). That is, the profit of the short call position for any given price for Asset X at the expiration date is the same as the loss of the long call position. Consequently, the maximum profit that the short call position can produce is the option price. The maximum loss is not limited because it is the highest price reached by Asset X on or before the expiration date, less the option price; this price can be indefinitely high. Exhibit 4.3 shows the profit/loss profile for a short call position.