Options: The Buyer's Right, the Seller's Duty

An optionIn finance, an option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option.Read on Wikipedia → gives its buyer the right to make a trade at an agreed price. The buyer pays for that right but does not have to use it. The seller receives the payment and accepts the corresponding obligation.

A call optionIn finance, a call option is an option contract that gives its buyer the right, but not the obligation, to buy an agreed quantity of a particular commodity, security, or other financial instrument from the seller at a specified price. The asset or instrument to which the option relates is known as the underlying, and the specified purchase price is known as the strike price. The right may be exercisable at or before a specified date, depending on the terms of the option.Read on Wikipedia → gives the right to buy an asset. A put optionIn finance, a put or put option is a derivative instrument in financial markets that gives the holder the right to sell an asset, at a specified price, by a specified date to the writer of the put. The purchase of a put option is interpreted as a negative sentiment about the future value of the underlying stock. The term "put" comes from the fact that the owner has the right to "put up for sale" the stock or index.Read on Wikipedia → gives the right to sell. The agreed price is the strike priceIn finance, the strike price of an option is a fixed price at which the owner of the option can buy, or sell, the underlying security or commodity. The strike price may be set by reference to the spot price, which is the market price of the underlying security or commodity on the day an option is taken out. Alternatively, the strike price may be fixed at a discount or premium.Read on Wikipedia →, and the amount paid for the option is the premiumIn finance, an option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option.Read on Wikipedia →. The right ends at the option’s expiry.

Following a call from purchase to expiry

In Hull’s historical Apple example, an investor buys a December call with a strike price of $340. The quoted premium is $20.30 per share, and the contract covers 100 shares. The investor therefore pays $2,030 for the right to buy those shares at $340 each.

Suppose the share price is $400 when the investor exercises that right. Buying 100 shares at $340 costs $34,000. Selling them at $400 brings in $40,000, giving a $6,000 difference.

That difference is the option’s payoffIn finance, an option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option.Read on Wikipedia →, before counting its purchase cost. The profit is smaller because the investor paid a premium:

Payoff = 100 × ($400 − $340) = $6,000
Profit = $6,000 − $2,030 = $3,970

If the option expires without being used and has not been sold, the investor loses the $2,030 premium. The purchase of the option itself cannot lose more than its premium, excluding fees. Exercising it can create a new position in the shares, which must be paid for and managed separately.

Why a useful option can still lose money

At expiry, a call can be worth exercising whenever the share price is above the strike. But that benefit may be too small to cover the premium.

In this example, the share price must exceed $360.30 for the call purchase to produce a profit at expiry, before fees and interest. At exactly $360.30, the $20.30 benefit per share only covers the $20.30 premium.

Before expiry, the investor may instead sell the option. That result depends on its market price at the time, which can include value for the remaining opportunity to exercise it later.

The seller takes on an obligation

The chapter also considers selling a September put with a $290 strike. The seller receives $12.70 per share, or $1,270 for a contract covering 100 shares. In return, the seller agrees to buy those shares at $290 if the option is exercised.

If the share price is $250 at exercise, the seller must pay $29,000 for shares worth $25,000. The $1,270 premium reduces that $4,000 loss, but does not remove it:

Profit = $1,270 − 100 × ($290 − $250) = −$2,730

This is why the buyer’s limit on loss does not apply to the seller. Selling an option can create losses much larger than the premium received.

Buying, selling, and using the right

Buying an option creates a long positionIn finance, a long position in a financial instrument means the holder of the position owns a positive amount of the instrument. The holder of the position has the expectation that the financial instrument will increase in value. This is known as a bullish position. The term "long position" is often used in context of buying options contracts.Read on Wikipedia →. Selling a new option creates a short positionIn finance, a position is the amount of a particular security, commodity or currency held or owned by a person or entity.Read on Wikipedia →, also called writing the option. This gives four basic positions: long call, short call, long put, and short put. Selling an option previously bought to close a long position is a different action from opening a short position.

The exercise rules also matter. A European-style optionIn finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options—as well as others where the payoff is calculated similarly—are referred to as "vanilla options". Options where the payoff is calculated differently are categorized as "exotic options". Exotic options can pose challenging problems in valuation and hedging.Read on Wikipedia → can be exercised only at expiry. An American-style optionIn finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options—as well as others where the payoff is calculated similarly—are referred to as "vanilla options". Options where the payoff is calculated differently are categorized as "exotic options". Exotic options can pose challenging problems in valuation and hedging.Read on Wikipedia → allows exercise earlier during the period set by its terms. The names describe the rules, not the country. The chapter’s Apple options are American; its simplified final-price profit graphs assume European exercise.

Writing the payoff as a formula

Let S_T be the share price at expiry and K the strike. Let c be the call premium per share and p the put premium. In the formulas, max(a, b) means choose the larger of the two values. It gives a zero payoff when using the right would provide no benefit.

Position	Payoff per share at expiry	Profit per share after premium
Long call	max(S_T − K, 0)	max(S_T − K, 0) − c
Short call	−max(S_T − K, 0)	c − max(S_T − K, 0)
Long put	max(K − S_T, 0)	max(K − S_T, 0) − p
Short put	−max(K − S_T, 0)	p − max(K − S_T, 0)

Multiply by the number of shares covered to find the whole position’s result. These formulas exclude fees and interest, as do the examples above. Contract sizes vary, so the 100-share size in these examples should not be assumed for every option.

Options trade on exchanges and in the over-the-counter (OTCOver-the-counter (OTC) or off-exchange trading or pink sheet trading is done directly between two parties, without the supervision of an exchange. It is contrasted with exchange trading, which occurs via exchanges. A stock exchange has the benefit of facilitating liquidity, providing transparency, and maintaining the current market price. In an OTC trade, the price is not necessarily publicly disclosed.Read on Wikipedia →) market. When comparing their prices, the strike and time remaining both matter. The chapter’s quotes show calls becoming cheaper as the strike rises and puts becoming more expensive. Those quotes also illustrate why price comparisons need the same contract terms: knowing only that something is “an option” says little about what it should cost.

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