# Call Option

Call option is a derivative financial instrument that entitles the holder to buy an asset (stock, bond, etc.) at a specified exercise price on the exercise date or any time before the exercise date.

Call option is a derivative instrument, which means its value depends on the price of the underlying asset. Unlike forward contracts and future contracts, which require no payment at their inception, a call option, like any other option, requires payment of upfront premium.

Call option is exercised only when it is in-the-money (which means that the price of the underlying asset is higher than the exercise price). For example, suppose we own a call option on the common stock of Apple, Inc. (NSYE: AAPL) with exercise price of \$400 and exercise date of today. Current price of AAPL stock is \$412.16; which means that we will earn \$12.16 by exercising the option to buy an AAPL share at \$400 and then immediately selling it in the market for \$412.16. This \$12.16 is the value of the option. The option will not be exercised when the price of the underlying asset (AAPL's stock) is lower than the exercise price.

A European call option can be exercised only at the exercise date while an American call option can be exercised at any time up to the exercise date.

A put option is the exact opposite of a call option.

## Payoff Formula

The value of a call option is the excess of the price at which we can sell that underlying asset in the open market (the underlying price) and the price at which we can buy the underlying asset (the exercise price).

The value of a call option can never be negative because it is an option and the holder is not under any obligation to exercise it if it has no positive value.

The following formula is used to calculate value of a call option.

Value of Call Option = max(0, underlying asset's price − exercise price)

## Example

Ben Jordan is a trader in an investment management firm. It is early May 20X3 and there is speculation that Intel is launching a new processor that is expected to improve performance and reduce power consumption drastically. He believes that this improvement can help revive the personal computer sales. However, he is not sure. He bought 5,000 call options on stock of Hewlett-Packard Company (NYSE: HP) and 1,000 call options on stock of Dell (NASDAQ: DELL).

Following table summarizes relevant information:

HP\$22\$24.2\$220-Jun-13
DELL\$14\$13.33\$120-Jun-13

Calculate the value of each option and tell which options Ben is most likely going to exercise? Calculate net profit, if any, on both call option trades.

Solution

Value of call option on HP stock = max(0, \$24.2 − \$22) = \$2.2

Total value of DELL call options = 5,000 × \$2.2 = \$11,000

Net profit on call option on HP stock = total option value − option cost = \$11,000 − 5,000 × \$2 = \$1,000

Value of call option on DELL stock = max (0, \$13.3 − \$14) = 0

Total value of DELL call options = 1,000 × 0 = 0

Net profit on call option on DELL stock = total option value − option cost = 0 − 1,000 × \$1 = -\$1,000

Ben is most likely going to exercise the call options on HP stock because they have positive values. Ben can exercise the options to purchase 5,000 HP stocks at \$22 per share and sell them in market for \$24.2 per share, realizing a total gain of \$11,000. However, this gain is reduced by the option cost, i.e. the premium paid up front.

He will let the options on Dell stock expire as they are worthless because it is not wise to buy Dell stock at \$14 when it is available in the market for \$13.3