Writing Call Options | Payoff | Example | Strategies

Writing call options, also called selling call options, refers to the decision that a party takes to sell an option. Options are one of the derivative instruments used in the world of finance in order to transfer risk from one entity to another and also can be used for hedging or arbitrage or speculation.

Call options are a financial instrument that gives its holder (buyer) the right but not the obligation to buy the underlying asset at a predetermined price during the period of the contract. Due to high potential liabilities in writing a call option, the writer has to maintain margin with its broker as well as with the exchange.

• Writing call options, also known as selling or shorting call options, involves the obligation to sell the underlying asset at a predetermined price (strike price) if the option holder exercises the option. Option writers receive a premium for taking on this obligation.
• Writing call options can be a strategy to generate income. By selling call options, investors can collect the premium upfront, providing a source of income.
• The potential profit is limited to the premium received when writing call options. If the underlying asset's price rises significantly, the option writer's profit potential is capped at the strike price plus the premium received.

Writing call options is a process of giving a holder the right but not the obligation to buy the shares at a predetermined price. Whereas, in writing a call option, a person sells the call option to the holder (buyer) and is obliged to sell the shares at the strike price if exercised by the holder. The seller, in return, receives a premium that is paid by the buyer.

This option makes parties have a contract prepared for an option dealing, whereby one could be compelled to buy the call option anytime before the expiration date of the security is achieved. The contract, in short, becomes an obligation for the parties involved.

This means if this agreement is agreed upon by the seller and buyer, neither of the parties can deny dealing when the time comes. If a buyer wants to buy the asset, the seller cannot deny it even if they get a better price from other buyers. Similarly, if the seller has to sell, the buyer cannot say refuse to deal even if they are getting the same thing at a cheaper rate.

Suppose two investors, Mr. A, and Mr. B, have done their research on the shares of TV Inc. Mr. A has 100 shares of TV Inc in his portfolio, and currently, TV Inc is trading at a price of $1000/-. Mr. A is pessimistic about the shares and feels that in one month’s time, TV Inc is going to trade at the same level, or it will drop from its current level and therefore wants to sell a call option. However, he wants to retain TV Inc’s shares in his portfolio for the long term. Hence, he places a sale of a call option on TV Inc for a strike price of $1200/-, at a premium of $400/-($4/per share) and a maturity of the next one month. The lot size of one contract we assume here is 100 shares.

On the other side, Mr. B feels that TV Inc S share is going to rise from $1000/- to $1200/-. And therefore, he wants to buy a call option. However, he does not wish to increase his portfolio as of now. Hence, he put his order to buy a call option on TV Inc for the strike price of $1200/-, at a premium of $400/- and a maturity period of the next month.

Mr. A found that someone has quoted a buy-on-call option with a bid price of $400/- for the strike price of $1200/-. He accepted the order, and the call option contract between the two got finalized.

During the maturity period, the price of TV Inc’s shares soars to $1300/- and hence Mr. B has exercised his call option (since the call option is in the money). Now, as per the contract, Mr. A has to sell 100 shares of TV Inc at a price of $1200/- to Mr. B, which would, in turn, be profitable for Mr. B as he can sell the shares at $1300/- in the spot market.

Here, Mr. B purchased the shares of TV Inc at a price of $1200/- which was worth $1300/- in the spot market. Whereas, Mr. A earned $400/- as Premium while writing the call option but had to sell the shares at $1200/- which was worth $1300/-.

In our example, an obvious question comes to our mind that if Mr. A feels that the shares of TV Inc are going to drop from its current level, then he could have bought a put option instead of selling a call option. In the case of buying a put option instead of writing a call option, he (as a holder) had to pay the Premium and would have lost the opportunity to earn the Premium by way of selling a call option.

With the above example, we can conclude that while writing a call option, the writer (seller) leaves his right and is obliged to sell the underlying at the strike price, if exercised by the buyer.

A call option gives the holder of the option the right to buy an asset by a certain date at a certain price. Hence, whenever a call option is written by the seller or writer, it gives a payoff of either zero since the call is not exercised by the holder of the option or the difference between the strike price and stock price, whichever is minimum. Below is the calculation that can help compute the payoff for these dealings:

Payoff of short call option = min(X – S_T, 0) or - max(S_T – X, 0)

We can calculate the payoff of Mr. A with the available details assumed in the above example.

• Payoff of Mr. A = min(X – S_T, 0)
• = min(1200 - 1300, 0)
• = - $100/-

Had the share price of TV Inc been moved to $1100/- and end up out of the money, the payoff for Mr. A would have been as follows

• Payoff of Mr. A = min(X – S_T, 0)
• = min(1200 - 1100, 0)
• = $0/-

A call option gives the holder the right but not the obligation to buy the shares at a predefined price during the life of the option. To write a call option, however, there are multiple strategies that can be taken into consideration.

In the above example, we have observed that Mr. A (writer of the call option) owns 100 shares of TV Inc. So when the option contract was exercised by Mr. B (the buyer of the call option), Mr. A had to sell the shares to Mr. B and closed the contract. But there would be a scenario wherein the underlying is not owned by the seller, or he is simply trading on the basis of his speculation. This argument gives space for Option Trading strategies involved in writing call options.

The strategy of writing call options can be done in two ways:

1. writing covered call
2. writing naked call or Naked short call

Let’s now discuss these two strategies involved in writing call options in detail.

#1 - Writing Covered Call

In writing a covered call strategy, the investor writes those call options for which s/he owns the underlying. This is a very popular strategy in writing options. This strategy is adopted by the investors if they feel that stock is going to fall or to be constant in the near term or short term but want to hold the shares in their portfolio.

As the share prices fall, they end up earning Premium. On the other hand, if the stock price rises, they sell the underlying to the buyer of call options.

In the above example, we have seen that Mr. A has written a call option on TV Inc shares which he is holding, and later sold the same to the buyer Mr. B since the share prices were not moved as per his expectation and the call option ended in the money. Here, Mr. A has covered his position by holding the underlying (shares of TV Inc). But had the share prices been moved as per his expectations and fallen down, he would have earned a net payoff of $400/- as Premium. However, in the case of a buyer, if share prices move up as per his expectation, he can earn unlimited profit theoretically.

In this way, the writer limits his losses by the difference between the strike price at which the underlying is sold and Premium earned by shorting or selling the call option.

Writing Covered Call Example

Suppose,

• S_T = $1200/-
• X = $1500/-
• C_O = 400/-

An investor has written the covered call option, and at the time of expiry, the stock price rose to $1600/-.

Payoff for the seller is as below:

• Pay-off = min(X - ST, 0)
• = max(1500 - 1600, 0)
• = -$100/-
• Net Payoff of writer = 400 - 100 = $300/-

#2 - Naked Writing Call or Naked Short Call

Writing a naked call is in contrast to a covered call strategy as the seller of the call options does not own the underlying securities. In other words, we can say that when the option is not combined with an offsetting position in the underlying stock.

In order to understand this, let’s think about another side of the transaction in call options where a person has written a call option and leaves the right to buy (or obliged to sell) a certain amount of shares at a certain price but does not own the underlying securities. This strategy is basically adopted by the investor when they are very speculative or think that share prices are not going to move upward.

In this type of strategy, the seller earns through Premium paid by the buyer. However, the losses would be unlimited theoretically, if share prices moved upward and exercised by the buyer. Therefore, there is limited profit with a huge potential of upside risk.

Further, the payoff for writing naked call options would be as similar as writing a covered call. The only difference is at the time of exercise by the buyer; the seller has to purchase the underlying from the market or alternatively has to borrow the shares from the broker and sell it to the buyer at the strike price.

Writing Naked Call Example

Let’s assume shares of ABC are currently trading at $800/- and the call option for a strike price of $1000/- with a maturity of one month and a Premium of $50/-. Here, I can sell a naked call (suppose I do not own shares of ABC) and earn an amount of $50/- through Premium. By doing so, I am deliberately speculating that the share price of ABC shall not move beyond $850/- ($800 + Premium of $50) till the expiration of the contract. In this strategy, I shall start incurring losses once ABC stock starts moving from the level of $850/- and it can be theoretically unlimited. Hence, there is a huge potential of making a loss through upside risk and limited potential of making a profit.

Let’s consider another example:

Suppose an investor sells a naked call option of XYZ stock for a strike price of $500/- at a premium of $10/- (since it is a short naked call option, he obviously doesn’t hold the shares of XYZ) with a maturity of one month.

Suppose, after one month, the share price of XYZ moves to $800/- on the expiry date. Since the option is in the money leading the same to be exercised by the buyer, the investor has to buy the shares of XYZ from the market at a price of $800/- and sell it to the buyer at $500/-. Here, the investor makes a loss of $300/-. Had the share price of XYZ been moved to $400/-, it would have earned the Premium as, in this scenario, options expire out of the money and will not be exercised by the buyer. The payoffs are summarized below.

The payoffs are summarized below.

This has been a guide to what is Writing Call Options. Here we discuss two strategies of writing call options along with an example. You may learn more about financing from the following articles –

• Call Option Examples
• IFRS vs. Indian GAAP
• Call Risk Examples
• Compare - Call Options vs. Put Options