# Call option, Call option purchase - International Financial Management

## Call option

The most well-known option contract is a call option for shares. It must be borne in mind that all stock options are associated with a certain number of shares, namely with 100 shares. When trading stocks, as a rule, a well-established tradition is realized - they are traded not individually, but blocks (which are called lots). Such a lot η mainly contains a certain number of shares, divisible by 100. This is the standard trading unit in the exchange trade. Of course, you have the right to purchase any other number of shares on the stock market, however, for buying less than 100 shares, you will have to pay higher commissions (per share). Thus, a call option is the right to buy 100 shares at a fixed price per share at any time (for the case of an American option), starting from the moment the option is acquired and until the expiration date is agreed. As a call option buyer, you acquire the above right, and as a call option seller, you grant the option to the buyer.

Fig. 4.1. Key positions in option transactions

Let's analyze the essence of the call option.

Example. There is a three-month European call option per share, the spot price of which is \$ 100. The exercise price of the option is \$ 100, the option is worth \$ 5. The investor acquires the option. This means that he pays the seller an option of \$ 5 and gets the right to buy from him in three months the share at the strike price, i.e. for \$ 100

Let's assume that the buyer of the option is a speculator who plays for promotion. He expects the stock price to increase by the time the contract expires to \$ 120. Let him be right. Then in three months the speculator executes the option, i.e. buys a share from the seller of the option for 100 and immediately sells it on the spot market for \$ 120. On the price difference, he wins \$ 20. The total gain of the speculator should be adjusted to the premium paid, so he will be

120 - 100 - 5 = \$ 15

Let the speculator make a mistake, and the share price fell to \$ 80 in three months. Then he will not execute the option, as it is unreasonable to buy the stock for \$ 100 on the option, if it is now on the market \$ 80. The result of the speculator's operation is loss premiums - 5 dollars

Consider an optional call agreement sequentially from the point of view of the buyer and the seller of the option.

## Purchase call option

The call option buyer hopes that the price of the corresponding shares will increase. By the way, by purchasing a call option for shares, its owner is not required to purchase relevant shares. In practice, the vast majority of call option buyers do not purchase shares themselves. The buyer has the time necessary to make an optimal decision, depending on the dynamics of the market price of the relevant shares and the duration of the period remaining until the expiration of the option. Let's analyze, taking into account all the above, all possible options for the investor's actions.

Stock prices are rising. Let's say you buy a call option for \$ 2 (\$ 200), which gives you the right to buy 100 shares of a certain company at \$ 80 each. If the shares rise in price above the strike price by \$ 4 (up to \$ 84), the option value also increases and will be, for example, 6 (600 dollars), which you can gain by selling the option at the moment. This will ensure that you receive the same profit that you would have recorded by investing \$ 8,000 in the purchase of 100 shares at \$ 80 each and then selling them at \$ 84 (however, this comparison ignores brokerage commissions that would be significantly higher if you transfer 100 of shares than one option).

The stock price is falling. Suppose now that in the initial conditions of the call option under consideration, by the time it expired, the value of the underlying asset fell to \$ 68 per share. You lost \$ 200. However, if you bought 100 shares, paying \$ 8,000 for them, your losses would be \$ 1,200, as each stock was \$ 12 cheaper.

Thus, the risks associated with buying an option are lower than when you invest directly in stocks. Of course, a shareholder can wait for a temporary drop in the price, and he can wait as long as he likes . But the holder of the shares has \$ 8000 associated ", and no one will say how long it will take for him to be able to make a profit, that is, the payment for owning shares is an opportunity cost, or missed opportunities - capital is invested, and time goes. The buyer of the option risks only a few months, and less.

Buying a call option, as it follows from the examples discussed above, provides the investor with the potential to control significant amounts of investments using relatively small amounts of cash. This effect is called leverage , which is perhaps the most important characteristic of option trades, since the purchase of options allows you to control hundreds of shares without linking large sums of money, leaving they are at risk. As for the real risks of the call option buyer, the limited amount of money that he invests in the acquisition of the option (compared to the acquisition of the corresponding number of base shares) reduces the one hundred risk in the event of adverse changes in stock prices: the potential losses of the investor are limited in this case the size of the premium paid. However, it is necessary to remember at the same time that the time factor in risk management works against the buyer of the call option.

A buyer of a call option will have an advantage over the owner of shares only as long as the option exists, and its expiration is a reality that can not be avoided. The owner of the shares risks large amounts of money, but he is not affected by the expiration date: he can in principle compensate for his losses, waiting for the restoration of the share price, even if it takes years. The buyer of the call option will incur losses if the value of the shares does not recover until the moment it expires. Therefore, there is no point in purchasing call options just for the sake of limiting risks.

Reasons for buying a call option There are many reasons why stock market participants can acquire the right to buy underlying options. Let's consider some of them.

1. Using the financial lever. The main attractive feature of buying a call is the ability to get a significant percentage profit, even from a moderate increase in the price of the underlying share.

Suppose that basic shares are worth \$ 200 per share, and a three-month call with a strike price of \$ 210 is worth \$ 30 per share. Let's assume that the rate of the shares in question will increase to \$ 260 in three months. Then the yield of buying the shares themselves at the current exchange rate with the aim of reselling them at the future rate will be 30%: (260-200): 200. If the investor buys a call option for \$ 30 ., and then it will perform, then the profitability of its financial transaction will be 66.7%: (260 - 210 - 30): 30. Thus, the profitability of the operation with the call option is more than two times higher than the yield of the usual cash transaction at a much lower cost of the advanced capital.

Let's consider one more example, illustrating the use of financial leverage, when the call option is not executed, but resold. Suppose that the underlying shares are worth \$ 48 per share, and a six-month call with a strike price of \$ 50 is \$ 3 per share. In this case, with the help of an investment of \$ 300, the investor can try to play at an increase in the price of the underlying stock within 6 months. If the stock rises in price by \$ 10 (slightly more than 20%), the call will cost at least \$ 8, i.е. \$ 800 per lot. When selling such an option, the seller of the call will receive a profit of 167% 1 with an increase in the share price of just over 20%.

2. Limit the maximum purchase price of shares in the future. If you, as an investor, acquire a call option, then essentially fixing the size of your possible future investment in a particular company's shares if, of course, decide to execute the option). Suppose that you would like to purchase 100 shares of the company of interest to you, experiencing some development difficulties recently. They are currently traded at \$ 39 per share, and you are sure that after the company successfully solves the problems of modernization, a deal made at such a price will undoubtedly be profitable. However, you do not have free at the moment \$ 3,900 and only after 6 months. you will have an amount sufficient to make such a purchase.

Not knowing what will happen in this period, but predicting the effective functioning of the company, you accept the only right decision in the circumstances under consideration to purchase the call option with the intention of executing it when you have the means to do it.

You acquire a corresponding call option with a strike price, say \$ 40 and a premium of \$ 3 (\$ 300), keeping track of the dynamics of the market rate of the shares of interest to you. Suppose that after 6 months. shares of the company in question rose to \$ 56 per share, and the call option was sold at a premium

16 (1600 loll.). In this case, the investor has a choice: either to sell the call option for 16 and immediately fix his income from the sale of the option in the amount of \$ 1600, or execute the option and buy 100 shares at \$ 40 per each.

The advantages of this strategy are that your investments are limited: if you make a mistake in your forecast and the stock becomes cheaper, then you will lose only the option premium. If you are right, you will receive 100 shares of the company of interest to you at a price much lower than the market rate.

3. Hedging in case of a fall in stock prices. A stock market participant, using a call option, can protect against possible losses as a result of the predicted drop in stock prices. For this, the shares that he owns must be sold with the simultaneous acquisition of the corresponding call option. Thus, the investor first of all will record the income from the shares. At the same time, being the holder of a call option, he will retain the opportunity, in the event of a rise in the price of the shares in question, to acquire them at a price below the market price.

4. Getting a speculative profit as a result of the expected increase in stock prices. Call options allow investors to receive high returns in an upward, or "bullish" stock market either from the game to the premium, or from the shares themselves in the event of the execution of the option agreement. In the latter case, the shares received when exercising the option for the sale of profits must be sold.

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