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Option Contracts

A call option is a contract that gives the owner the right to buy a financial instrument at the exercise price within a specific period of time. A put option is a contract that gives the owner the right to sell a financial instrument at the exercise price within a specific period of time.

Profits and Losses on Option and Futures Contracts

To understand option contracts more fully, let's first examine the option on the same June Treasury bond futures contract that we looked at earlier in the chapter. Recall that if you buy this futures contract at a price of 115 (that is, $115,000), you have agreed to pay $115,000 for $100,000 face value of long-term Treasury bonds when they are delivered to you at the end of June. If you sold this futures contract at a price of 115, you agreed, in exchange for $115,000, to deliver $100,000 face value of the long-term Treasury bonds at the end of June. An option contract on the Treasury bond futures contract has several key features: (1) It has the same expiration date as the underlying futures contract, (2) it is an American option and so can be exercised at any time before the expiration date, and (3) the premium (price) of the option is quoted in points that are the same as in the futures contract, so each point corresponds to $1,000. If, for a premium of $2,000, you buy one call option contract on the June Treasury bond contract with an exercise price of 115, you have purchased the right to buy (call in) the June Treasury bond futures contract for a price of 115 ($115,000 per contract) at any time through the expiration date of this contract at the end of June. Similarly, when for $2,000 you buy a put option on the June Treasury bond contract with an exercise price of 115, you have the right to sell (put up) the June Treasury bond futures contract for a price of 115 ($115,000 per contract) at any time until the end of June.

Futures option contracts are somewhat complicated, so to explore how they work and how they can be used to hedge risk, let's first examine how profits and losses on the call option on the June Treasury bond futures contract occur. In February, our old friend Irving the Investor buys, for a $2,000 premium, a call option on the $100,000 June

Treasury bond futures contract with a strike price of 115. (We assume that if Irving exercises the option, it is on the expiration date at the end of June and not before.) On the expiration date at the end of June, suppose that the underlying Treasury bond for the futures contract has a price of 110. Recall that on the expiration date, arbitrage forces the price of the futures contract to be the same as the price of the underlying bond, so it too has a price of 110 on the expiration date at the end of June. If Irving exercises the call option and buys the futures contract at an exercise price of 115, he will lose money by buying at 115 and selling at the lower market price of 110. Because Irving is smart, he will not exercise the option, but he will be out the $2,000 premium he paid. In such a situation, in which the price of the underlying financial instrument is below the exercise price, a call option is said to be "out of the money." At the price of 110 (less than the exercise price), Irving thus suffers a loss on the option contract of the $2,000 premium he paid. This loss is plotted as point A in panel (a) of Figure 1.

On the expiration date, if the price of the futures contract is 115, the call option is "at the money," and Irving is indifferent whether he exercises his option to buy the futures contract, because exercising the option at 115 when the market price is also at 115 produces no gain or loss. Because he has paid the $2,000 premium, at the price of 115 his contract again has a net loss of $2,000, plotted as point B.

If the futures contract instead has a price of 120 on the expiration day, the option is "in the money," and Irving benefits from exercising the option: He would buy the futures contract at the exercise price of 115 and then sell it for 120, thereby earning a 5-point gain ($5,000 profit) on the $100,000 Treasury bond contract. Because Irving paid a $2,000 premium for the option contract, however, his net profit is $3,000 ($5,000 — $2,000). The $3,000 profit at a price of 120 is plotted as point C. Similarly, if the price of the futures contract rose to 125, the option contract would yield a net profit of $8,000 ($10,000 from exercising the option minus the $2,000 premium), plotted as point D. Plotting these points, we get the kinked profit curve for the call option that we see in panel (a).

Suppose that instead of purchasing the futures option contract in February, Irving decides instead to buy the $100,000 June Treasury bond futures contract at the price of 115. If the price of the bond on the expiration day at the end of June declines to 110, meaning that the price of the futures contract also falls to 110, Irving suffers a loss of 5 points, or $5,000. The loss of $5,000 on the futures contract at a price of 110 is plotted as point A' in panel (a). At a price of 115 on the expiration date, Irving would have a zero profit on the futures contract, plotted as point B'. Ata price of 120, Irving would have a profit on the contract of 5 points, or $5,000 (point C'), and at a price of 125, the profit would be 10 percentage points, or $10,000 (point D'). Plotting these points, we get the linear (straight-line) profit curve for the futures contract that appears in panel (a).

Now we can see the major difference between a futures contract and an option contract. As the profit curve for the futures contract in panel (a) indicates, the futures contract has a linear profit function: Profits grow by an equal dollar amount for every point increase in the price of the underlying financial instrument. By contrast, the kinked profit curve for the option contract is nonlinear, meaning that profits do not always grow by the same amount for a given change in the price of the underlying financial instrument. The reason for this nonlinearity is that the call option protects Irving from having losses that are greater than the amount of the $2,000 premium. In contrast, Irving's loss on the futures contract is $5,000 if the price on the expiration day falls to 110, and if the price falls even further, Irving's loss will be even greater. This insurance-like feature of option contracts explains why their purchase price is referred to as a premium. Once the underlying financial instrument's price rises above the exercise price, however,

Profits and Losses on Options Versus Futures Contracts

FIGURE 1 Profits and Losses on Options Versus Futures Contracts

The futures contract is the $100,000 June Treasury bond contract, and the option contracts are written on this futures contract with an exercise price of 115. Panel (a) shows the profits and losses for the buyer of the call option and the buyer of the futures contract, and panel (b) shows the profits and losses for the buyer of the put option and the seller of the futures contract.

Irving's profits grow linearly. Irving has given up something by buying an option rather than a futures contract. As we see in panel (a), when the price of the underlying financial instrument rises above the exercise price, Irving's profits are always less than that on the futures contract by exactly the $2,000 premium he paid.

Panel (b) plots the results of the same profit calculations if Irving buys not a call but a put option (an option to sell) with an exercise price of 115 for a premium of $2,000 and if he sells the futures contract rather than buying one. In this case, if on the expiration date the Treasury bond futures have a price above the 115 exercise price, the put option is "out of the money." Irving would not want to exercise the put option and then have to sell the futures contract he owns as a result at a price below the market price and lose money. He would not exercise his option, and he would be out only the $2,000 premium he paid. Once the price of the futures contract falls below the 115 exercise price, Irving benefits from exercising the put option because he can sell the futures contract at a price of 115 but can buy it at a price below this. In such a situation, in which the price of the underlying instrument is below the exercise price, the put option is "in the money," and profits rise linearly as the price of the futures contract falls. The profit function for the put option illustrated in panel (b) of Figure 1 is kinked, indicating that Irving is protected from losses greater than the amount of the premium he paid. The profit curve for the sale of the futures contract is just the negative of the profit for the futures contract in panel (a) and is therefore linear.

Panel (b) of Figure 1 confirms the conclusion from panel (a) that profits on option contracts are nonlinear but profits on futures contracts are linear.

Two other differences between futures and option contracts must be mentioned. The first is that the initial investment on the contracts differs. As we saw earlier in the chapter, when a futures contract is purchased, the investor must put up a fixed amount, the margin requirement, in a margin account. But when an option contract is purchased, the initial investment is the premium that must be paid for the contract. The second important difference between the contracts is that the futures contract requires money to change hands daily when the contract is marked to market, whereas the option contract requires money to change hands only when it is exercised.

 
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