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Call Option

By Yuriy Smirnov Ph.D.

Definition

A call option is a contract that can be traded in both exchange and the over-the-counter (OTC) market. The buyer (also referred to as holder) of a call option gets the right but not the obligation to buy a set amount of underlying asset at a predetermined price (called strike price) within a time period before the expiration date. In turn, the writer of a contract (also referred to as seller) is liable to sell a specified amount of underlying asset at the strike price if the buyer decides to exercise his right. In turn, the buyer has to pay the seller a certain amount of money called premium to buy a call option.

Important! The time lapse when a call option can be exercised depends on its style. An American-style option gives the buyer the right to exercise it at any time before the expiration date, but a European-style option can be exercised only on the expiration date.

Value of a call option

The value (premium) of a call option consists of two components:

Intrinsic value

The intrinsic value represents the payoff that the buyer would receive if the contract were exercised immediately. Thus, the intrinsic value depends on the difference between the strike price and the spot price of the underlying asset. From this point of view, three situations may arise.

  1. If the spot price is higher than the strike price, then the call option is in the money, and its intrinsic value is positive. The buyer has the right to buy the underlying asset at a strike price that is lower than the current spot price, benefiting from the price difference.
  2. If the strike price is higher than the spot price, the call option is out of the money. It makes no sense for the buyer to exercise the contract, so the intrinsic value will be equal to zero.
  3. If the strike price equals the spot price, the call option is at the money, but its intrinsic value is also zero.

Important! Please note that the intrinsic value of an option can’t be a negative value. It can be either positive or equal to zero.

Time value

The extrinsic or time value of an option is the difference between its premium and intrinsic value. In other words, time value measures the influence of other factors than the price of the underlying asset. The main factors affecting the time value are as follows:

The time value gradually decreases as the expiration date approaches. In other words, the farther the expiration date is from the present moment in time, the higher the time value of an option will be.

The price volatility of the underlying asset also has a strong effect on time value. The greater the price volatility of the underlying asset, the higher the time value and vice versa.

The time value of an option at the moment t can be calculated using the following formulas:

Premiumt = Intrinsic Valuet + Time Valuet

Time Valuet = Premiumt – Intrinsic Valuet

Let’s suppose the call option for 100 shares of Apple Inc. at a strike price of $ 216.25. The premium is $13.75 per share, and the spot price of underlying stock is $220.76.

As far as the strike price is lower than the spot price, the call option is in the money and has a positive intrinsic value.

Intrinsic value = ($220.76 - $216.25) × 100 = $451

Time value = $13.75 × 100 - $451 = $924

Call option payoff diagram

As we already know, the key feature of a call option is that this contract implies asymmetric rights and liabilities for a writer and a buyer. As a result, the payoff diagram of a buyer and of a writer will be different. Let's look at the example below.

Example

Suppose an investor has bought an American-style call option for 100 shares of Facebook, Inc. at a strike price of $175.50. The premium paid was $12.35 per share. Let’s plot a payoff diagram for both the buyer and the writer.

Buyer’s payoff diagram

When an investor purchases a call option, he or she expects that the price of the underlying asset will rise above the strike price. At the same time, the investor will avoid losses if the price of the underlying asset drops below the strike price. It would not have been possible if he had directly bought 100 shares of Facebook, Inc.

Let’s go through two alternative scenarios.

  1. Scenario A: spot price rises to $200,00 per share
  2. Scenario B: spot price drops to $160,00 per share

Under Scenario A, the call option is in the money. If the buyer exercises his right to buy 100 shares of Facebook, Inc., his or her profit amounts to $1,215.

[($200.00 - $175.50) × 100 - $12.35 × 100] = $1,215

However, if the investor acquired 100 shares of Facebook, Inc. at a price of $175.50, his or her profit would be $2,450.

($200.00 - $175.50) × 100 = $2,450

Important! Option has a lower payoff because of the premium.

Under Scenario B, the call option ends up out of the money. Thus, the loss of the buyer equals the premium of $1,235 ($12.35 × 100) paid to the seller (writer).

However, if the investor bought 100 shares at $ 175.50, his or her loss would amount to $2,450.

($160.00 - $175.50) × 100 = -$1,550

As we can see, buying a call option will limit the losses of the investor by the amount of premium paid if the spot price of the underlying asset drops below the strike price.

These relationships are illustrated in the diagram below.

Long call option payoff diagram

If the price of the underlying asset is under the strike price, the call option will be out of the money, and the loss for the buyer will be equal to the amount of the premium paid to the writer.

If the spot price is higher than the strike price, the call option will be in the money, but the buyer will still incur losses until the spot price reaches the breakeven point, which equals the sum of the strike price and the premium per share. In the example above, the breakeven point amounts to $187.85 ($175.50 + $12.35).

At any spot price above the breakeven point, the buyer will get a profit.

Important! The loss of the buyer of the call option is always limited by the amount of premium paid. At the same time, the amount of profit that can be earned is not limited.

Writer’s payoff diagram

As far as a call option is a contract that gives the writer and buyer different rights and liabilities, the writer pursues different goals than the buyer. An investor can write a call option due to two reasons.

  1. Speculation. If an investor expects that the price of the underlying asset will not rise above the strike price, he or she can write a call option. If it ends up out of the money, the investor will get a profit equal to the amount of the premium received.
  2. Reducing underlying asset acquisition costs. Let’s assume an investor has previously bought 100 shares. If the sideways or weak bearish trend prevails on the market, the investor can write a call option. If the call option ends up out of the money, the profit of the writer will amount to the premium received. In this case, the investor will manage to reduce the actual shares acquisition costs.

The writer’s payoff diagram is presented in the figure below.

Short call option payoff diagram

At any level where the spot price is below the strike price, a call option is out of the money. In such a case, the profit of the writer equals the amount of premium received.

If the spot price of the underlying stock exceeds the strike price, the buyer will exercise the contract. However, even in this situation, the writer will earn a profit if the spot price does not exceed the breakeven point.

When the spot price rises above the breakeven point, the writer will face losses.

Important! The writer’s profit is limited by the amount of the premium received. However, the amount of losses depends on whether the call option is covered or uncovered.

Covered call option

The call option is considered to be covered if the writer possesses the required number of underlying stocks specified in the contract.

To better understand the issue, let’s consider the example below.

Let’s assume that some time ago an investor acquired 100 shares of General Motors Company at a price of $ 32.50 per share. Now the investor believes that the stock price will not rise in the next few months, so he decides to reduce the acquisition cost by writing a 3-month European call option at a strike price of $32.35 and a premium of $3.65 per share.

Let’s consider two alternative scenarios. when spot price at the expiration date reaches

  1. Scenario A: spot price at the expiration date drops to $30,23
  2. Scenario B: spot price at the expiration date rises to $37,11

Under Scenario A, the investor’s expectations will be met, and the call option ends up out of the money. The investor will also make a profit of $ 3.65 per 1 share, which will actually reduce the purchase price of shares to $28.85 ($32.50 - $3.65).

Under Scenario B, the call option will end up in the money, so the buyer will ask to exercise the contract. In turn, the writer is liable to sell 100 shares of General Motors Company at a strike price of

$32.35. However, the investor already has the number of shares required to exercise the contract. In this situation, the writer will not incur any losses but will earn a profit of $350.

($32.35 + $3.65 - $32.50) × 100 = $350

As far as the investor bought these shares earlier at $32.50, he does not have to buy them at the spot price of $37.11. The actual amount of loss due to the price difference will be $0.15 per share ($32.35 - $32.50), but this loss is fully covered by proceeds from the premium received, so the actual profit of the investor will be $3.50 per share ($3.65 - $0.15).

However, the investor will face a loss of profit, which should be taken into account. If the call option had not been written, the investor would not have received a premium but would have earned $4.61 per share ($37.11 - $32.50) as capital gains. Thus, the lost profit totals $1.11 per share ($4.61 - $3.50).

Important! The maximum loss for the writer of a covered call option is known in advance. It is defined by three components:

All of these components are known at the moment when a call option is written and are not subject to change in the future.

Uncovered call option

If the writer does not possess any underlying asset, a call option is considered to be uncovered. To settle the contract, the writer has to buy the underlying asset at the spot price and sell it to the buyer at the strike price. In such case, the amount of loss is not limited and depends on the difference between the spot price and the strike price.

Let’s consider the previous example assuming that the investor does not own any underlying shares. Under Scenario B, the call option expires in the money. To settle the contract, the writer has to buy 100 shares of General Motors Company at the spot price of $37.11 and sell them to the buyer at a strike price of $32.35. The loss amounts to $111.

($32.35 + $3.65 - $37.11) × 100 = -$111

As we can see, the loss of a call option writer is not limited. The higher the spot price, the greater will be the writer’s loss.