Puts and Calls

In finance, an option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy or sell an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option. Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction. Thus, they are also a form of asset and have a valuation that may depend on a complex relationship between underlying asset value, time until expiration, market volatility, and other factors. Options may be traded between private parties in over-the-counter (OTC) transactions, or they may be exchange-traded in live, orderly markets in the form of standardized contracts.

Definition and application

An option is a contract that allows the holder the right to buy or sell an underlying asset or financial instrument at a specified strike price on or before a specified date, depending on the form of the option. The strike price may be set by reference to the spot price (market price) of the underlying security or commodity on the day an option is issued, or it may be fixed at a discount or at a premium. The issuer has the corresponding obligation to fulfill the transaction (to sell or buy) if the holder "exercises" the option. An option that conveys to the holder the right to buy at a specified price is referred to as a call, while one that conveys the right to sell at a specified price is known as a put.

The issuer may grant an option to a buyer as part of another transaction (such as a share issue or as part of an employee incentive scheme), or the buyer may pay a premium to the issuer for the option. A call option would normally be exercised only when the strike price is below the market value of the underlying asset, while a put option would normally be exercised only when the strike price is above the market value. When an option is exercised, the cost to the option holder is the strike price of the asset acquired plus the premium, if any, paid to the issuer. If the option’s expiration date passes without the option being exercised, the option expires, and the holder forfeits the premium paid to the issuer. In any case, the premium is income to the issuer, and normally a capital loss to the option holder.

The holder of an option may on-sell the option to a third party in a secondary market, in either an over-the-counter transaction or on an options exchange, depending on the option. The market price of an American-style option normally closely follows that of the underlying stock being the difference between the market price of the stock and the strike price of the option. The actual market price of the option may vary depending on a number of factors, such as a significant option holder needing to sell the option due to the expiration date approaching and not having the financial resources to exercise the option, or a buyer in the market trying to amass a large option holding. The ownership of an option does not generally entitle the holder to any rights associated with the underlying asset, such as voting rights or any income from the underlying asset, such as a dividend.


Historical uses of options

Contracts similar to options have been used since ancient times.[1] The first reputed option buyer was the ancient Greek mathematician and philosopher Thales of Miletus. On a certain occasion, it was predicted that the season's olive harvest would be larger than usual, and during the off-season, he acquired the right to use a number of olive presses the following spring. When spring came and the olive harvest was larger than expected, he exercised his options and then rented the presses out at a much higher price than he paid for his 'option'.[2][3]

The 1688 book Confusion of Confusions describes the trading of "opsies" on the Amsterdam stock exchange, explaining that "there will be only limited risks to you, while the gain may surpass all your imaginings and hopes."[4]

In London, puts and "refusals" (calls) first became well-known trading instruments in the 1690s during the reign of William and Mary.[5] Privileges were options sold over the counter in nineteenth century America, with both puts and calls on shares offered by specialized dealers. Their exercise price was fixed at a rounded-off market price on the day or week that the option was bought, and the expiry date was generally three months after purchase. They were not traded in secondary markets.

In the real estate market, call options have long been used to assemble large parcels of land from separate owners; e.g., a developer pays for the right to buy several adjacent plots, but is not obligated to buy these plots and might not unless they can buy all the plots in the entire parcel.

In the motion picture industry, film or theatrical producers often buy an option giving the right — but not the obligation — to dramatize a specific book or script.

Lines of credit give the potential borrower the right — but not the obligation — to borrow within a specified time period.

Many choices, or embedded options, have traditionally been included in bond contracts. For example, many bonds are convertible into common stock at the buyer's option, or may be called (bought back) at specified prices at the issuer's option. Mortgage borrowers have long had the option to repay the loan early, which corresponds to a callable bond option.

Modern stock options

Options contracts have been known for decades. The Chicago Board Options Exchange was established in 1973, which set up a regime using standardized forms and terms and trade through a guaranteed clearing house. Trading activity and academic interest has increased since then.

Today, many options are created in a standardized form and traded through clearing houses on regulated options exchanges, while other over-the-counter options are written as bilateral, customized contracts between a single buyer and seller, one or both of which may be a dealer or market-maker. Options are part of a larger class of financial instruments known as derivative products, or simply, derivatives.[6][7]

Contract specifications

A financial option is a contract between two counterparties with the terms of the option specified in a term sheet. Option contracts may be quite complicated; however, at minimum, they usually contain the following specifications:[8]

  • whether the option holder has the right to buy (a call option) or the right to sell (a put option)
  • the quantity and class of the underlying asset(s) (e.g., 100 shares of XYZ Co. B stock)
  • the strike price, also known as the exercise price, which is the price at which the underlying transaction will occur upon exercise
  • the expiration date, or expiry, which is the last date the option can be exercised
  • the settlement terms, for instance whether the writer must deliver the actual asset on exercise, or may simply tender the equivalent cash amount
  • the terms by which the option is quoted in the market to convert the quoted price into the actual premium – the total amount paid by the holder to the writer

Call Option

A trader who expects a stock's price to increase can buy a call option to purchase the stock at a fixed price (strike price) at a later date, rather than purchase the stock outright. The cash outlay on the option is the premium. The trader would have no obligation to buy the stock, but only has the right to do so on or before the expiration date. The risk of loss would be limited to the premium paid, unlike the possible loss had the stock been bought outright.

The holder of an American-style call option can sell the option holding at any time until the expiration date, and would consider doing so when the stock's spot price is above the exercise price, especially if the holder expects the price of the option to drop. By selling the option early in that situation, the trader can realise an immediate profit. Alternatively, the trader can exercise the option — for example, if there is no secondary market for the options — and then sell the stock, realising a profit. A trader would make a profit if the spot price of the shares rises by more than the premium. For example, if the exercise price is 100 and premium paid is 10, then if the spot price of 100 rises to only 110 the transaction is break-even; an increase in stock price above 110 produces a profit.

The holder of an European-style call option can only sell the option at the expiration date. If the stock price at expiration is lower than the exercise price, the holder of the option at that time will let the call contract expire and lose only the premium (or the price paid on transfer).

Mathematically, the payoff -- when it occurs-- of a call option equals

[[math]] \max\{(S-K), 0\} [[/math]]

where [math]K[/math] is the strike price and [math]S[/math] is the spot price of the underlying asset.

Long call option.svg.png

Put Option

A trader who expects a stock's price to decrease can buy a put option to sell the stock at a fixed price (strike price) at a later date. The trader is under no obligation to sell the stock, but has the right to do so on or before the expiration date. If the stock price at expiration is below the exercise price by more than the premium paid, the trader makes a profit. If the stock price at expiration is above the exercise price, the trader lets the put contract expire, and loses only the premium paid. In the transaction, the premium also plays a role as it enhances the break-even point. For example, if the exercise price is 100 and the premium paid is 10, then a spot price between 90 and 100 is not profitable. The trader makes a profit only if the spot price is below 90.

The trader exercising a put option on a stock does not need to own the underlying asset, because most stocks can be shorted.

Mathematically, the payoff -- when it occurs-- of a put option equals

[[math]]\max\{(K-S), 0\}[[/math]]

where [math]K[/math] is the strike price and [math]S[/math] is the spot price of the underlying asset.

Long put option.svg.png


  1. Abraham, Stephan (May 13, 2010). "History of Financial Options - Investopedia". Investopedia. Retrieved Jun 2, 2014.
  2. Mattias Sander. Bondesson's Representation of the Variance Gamma Model and Monte Carlo Option Pricing. Lunds Tekniska Högskola 2008
  3. Aristotle. Politics.
  4. Josef de la Vega. Confusion de Confusiones. 1688. Portions Descriptive of the Amsterdam Stock Exchange Selected and Translated by Professor Hermann Kellenbenz. Baker Library, Harvard Graduate School Of Business Administration, Boston, Massachusetts.
  5. Smith, B. Mark (2003), History of the Global Stock Market from Ancient Rome to Silicon Valley, University of Chicago Press, p. 20, ISBN 0-226-76404-4
  6. Brealey, Richard A.; Myers, Stewart (2003), Principles of Corporate Finance (7th ed.), McGraw-Hill, Chapter 20
  7. Hull, John C. (2005), Options, Futures and Other Derivatives (excerpt by Fan Zhang) (6th ed.), Pg 6: Prentice-Hall, ISBN 0-13-149908-4CS1 maint: location (link)
  8. Characteristics and Risks of Standardized Options, Options Clearing Corporation, retrieved July 15, 2020