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Option (finance)

From Wikipedia, the free encyclopedia

(Redirected from Stock option)

For other uses, see Option

An option contract is an agreement in which the buyer (holder) has the right (but not the obligation) to exercise by buying or selling an asset at a set price (strike price) on or before a future date (the exercise date or expiration); and the seller (writer) has the obligation to honor the terms of the contract. Since the option gives the buyer a right and the writer an obligation, the buyer pays the option premium to the writer. The buyer is considered to have a long position, and the seller a short position.

Given that the contract's value is determined by an underlying asset and other variables, it is classified as a derivative.

For every open contract there is a buyer and a seller. Traders in exchange-traded options do not usually interact directly, but through a clearing house such as, in the U.S., the Options Clearing Corporation (OCC). The OCC guarantees that an assigned writer will fulfill his obligation if the option is exercised.

The contract specifies

  • whether it is a put option or call option. Put options give the holder the right to sell the asset at the strike price. Call options give the holder the right to purchase the asset at the strike price.
  • the underlying security (e.g. XYZ Co.)
  • the strike price or exercise price. It can be specified, or based on a reference rate, or measured at agreed-upon intervals during the life of the contract.
  • the date that will be either the last possible date for exercise (American options) , or the only date for exercise (European options). This date is commonly known as the expiration date.
  • the quantity of the security included in each contract. This is standard and predetermined by the exchanges for traded options, e.g. common share options have 100 shares in 1 contract.
  • the ratio of actual settlement price to the price quoted in the market, also known as the 'multiplier'.

Example: a call option on 100 shares (one contract) of (NY-JNJ) at strike price $54.00 to expire Dec2007 with a multiplier of 100. 1 JNJ Dec Call $54

Types of options

  • Real option (real option) is a choice that an investor has when investing in the real economy (i.e. in the production of goods or services, rather than in financial contracts). This option may be something as simple as the opportunity to expand production, or to change production inputs. Real options are an increasingly influential tool in corporate finance. They are typically difficult or impossible to trade, and lack the liquidity of exchange-traded options.
  • Traded options (also called "Exchange-Traded Options" or "Listed Options") is a class of Exchange traded derivatives. As for other classes of exchange traded derivatives, trade options have standardized contracts, quick systematic pricing, and are settled through a clearing house (ensuring fulfillment). Trade options include
  1. stock options, discussed below,
  2. commodity options,
  3. bond options,
  4. interest rate options
  5. index (equity) options,
  6. currency cross rate options, and
  7. swaption.
  • Vanilla options are 'simple', well understood, and traded options; Exotic options are more complex, or less easily understood. Asian options, lookback options, barrier options are considered to be exotic, especially if the underlying instrument is more complex than simple equity or debt.
  • Employee stock options (employee stock option) are issued by a company to its employees as compensation.


The premium for an option contract is ultimately determined by supply and demand, but is influenced by five principal factors:

  • The price of the underlying security in relation to...
  • The strike price. Options will be in-the-money when there is a positive intrinsic value; when the strike price is above/below (put/call) the security's current price. They will be at-the-money when the strike price equals the security's current price. They will be out-of-the-money when the strike price is below/above (put/call) the security's current price. Options at-the-money or out-of-the-money have an intrinsic value of zero.
  • The cumulative cost required to hold a position in the security (including interest + dividends).
  • The time to expiration. The time value decreases to zero at its expiration date. The option style determines when the buyer may exercise the option. Generally the contract will either be American style - which allows exercise up to the expiration date - or European style - where exercise is only allowed on the expiration date - or Bermudan style - where exercise is allowed on several, specific dates up to the expiration date. European contracts are easier to value. Due to the "American" style option having the advantage of an early exercise day (i.e. at any time on or before the options expiry date), they are always at least as valuable as the "European" style option (only exercisable at the expiration date).
  • The estimate of the future volatility of the security's price. This is perhaps the least-known input into any pricing model for options, therefore traders often look to the marketplace to see what the implied volatility of an option is -- meaning that given the price of an option and all the other inputs except volatility you can solve for that value.

Pricing models include the binomial options model for American options and the Black-Scholes model for European options. Even though there are pricing models, the value of an option is a personal decision, requiring multiple trade offs and depending on the investment objective. See the Excel model [1] for the metrics of a call option.

Because options are derivatives, they can be combined with different combinations of

  • other options
  • risk free T-bills
  • the underlying security, and
  • futures contracts on that security

to create a risk neutral portfolio (zero risk, zero cost, zero return). In a liquid market, arbitrageurs ensure that the values of all these assets are 'self-leveling', i.e. they incorporate the same assumptions of risk/reward. In theory traders could buy cheap options and sell expensive options (relative to their theoretical prices), in quantities such that the overall delta is zero, and expect to make a profit. Nevertheless, implementing this in practice may be difficult because of "stale" stock prices, large bid/ask spreads, market closures and other symptoms of stock market illiquidity. If stock market prices do not follow a random walk (due, for example, to insider trading) this delta neutral strategy or other model-based strategies may encounter further difficulties. Even for veteran traders using very sophisticated models, option trading is not an easy game to play.

History of valuation

Models of option pricing were very simple and incomplete until 1973 when Fischer Black and Myron Scholes published the Black-Scholes pricing model. Scholes received the 1997 Bank of Sweden Prize in Economic Sciences (Nobel Prize of Economics) for this work, along with Robert C. Merton. In a departure from tradition, Fischer Black was specifically mentioned in the award, even though he had died and was therefore not eligible.

The Black-Scholes model gives theoretical values for European put and call options on non-dividend paying stocks. The key argument is that traders could risklessly hedge a long options position with a short position in the stock and continuously adjust the hedge ratio (the delta value -- one of the option sensitivities known as "greeks") as needed. Assuming that the stock price follows a random walk, and using the methods of stochastic calculus, a price for the option can be calculated where there is no arbitrage profit. This price depends only on 5 factors: the current stock price, the exercise price, the risk-free interest rate, the time until expiration, and the volatility of the stock price. Eventually, the model was adapted to be able to price options on dividend paying stocks as well.

The availability of a good estimate of an option's theoretical price contributed to the explosion of trading in options. Other option pricing models have since been developed for other markets and situations using similar arguments, assumptions, and tools, including the Black model for options on futures, Monte Carlo methods, Path Integrals, and Binomial options models.


Risk is concerned with the unknown. Upside risk is the possibility of gain. Downside risk is the possibility of loss. One half the reasons to use options (like other derivatives) is to reduce risk. Certainty is exchanged with other players who assume the risk in hope of big gains. It is wrong to state that "options are risky."

  • reduce risk: The seller of a covered call exchanges his upside risk (gains above the strike price) for the certainty of cash in hand (the premium). The buyer of a covered put limits his downside risk for a price - just like buying fire insurance for your house.
  • increase risk: The buyer of a call wants the upside risk of an asset, but will only pay a small percentage of its current value, so his returns are leveraged. The seller of a put accepts the downside risk of locking in his purchase price of an asset, in exchange for the premium.

To understand risk, look at the four standard graphs of options (put-call-buy-sell). The value of the options in the interim between purchase and expiration will not be exactly like these graphs, but close enough. In all cases, the premium was a certainty.

  • Buyers start out-of-pocket. But going forward, the option buyer has no downsider risk. The graph either flat lines or goes up on either side of the spot price.
  • Sellers start with a gain. Going forward, they have no upside risk. These graphs either flat line or go down on either side of the spot price.

The extent of risk varies. Buyers/sellers of calls have unlimited upside/downside risk as the asset price increases. Buyers/sellers of puts have upside/downside risk limited to the spot price of the asset (less the premium).

The year 2006 has shown that options again didn't live up to the "weapons of mass financial destruction" moniker detractors have given it. [2]


The most common way to trade stock options is trading standardized options contracts that are listed by various futures and options exchanges -- there are currently six exchanges in the United States that list standardized options contracts based on underlying stocks -- The Philadelphia Stock Exchange (PHLX), American Stock Exchange (AMEX) and NYSE Arca in New York City, and the Chicago Board Options Exchange (CBOE) which are all open-outcry marketplaces, and the International Securities Exchange (ISE) and Boston Options Exchange (BOX) are electronic marketplaces. However, even for the non-electronic exchanges, competition and the introduction of automated execution (AutoEx) has led, by late 2006, to hybridization where all but the largest trades are executed electronically. In Europe the main exchanges where stock options are traded are Euronext.liffe and Eurex.

There are also over-the-counter options contracts that are traded not on exchanges, but between two independent parties. At least one of those parties is usually a large financial institution with a balance sheet big enough to underwrite such a contract.

Option naming conventions

Stock option names are written in the following format: SYMBOL+MONTH+STRIKE

  • SYMBOL = Option Root Symbol
  • MONTH = Month the option expires
  • STRIKE = Strike price

Expiration Month Codes

Strike Price Codes

The basic trades or traded stock options

Payoffs and profits from a long call.
Payoffs and profits from a long call.
Payoffs and profits from a short call.
Payoffs and profits from a short call.
Payoffs and profits from a long put.
Payoffs and profits from a long put.
Payoffs and profits from a short put.
Payoffs and profits from a short put.

These trades are described from the point of view of a speculator. If they are combined with other positions, they can also be used in hedging.

Long Call
A trader who believes that a stock's price will increase might buy the right to purchase the stock (a call option) rather than just buy the stock. He would have no obligation to buy the stock, only the right to do so until the expiry date. If the stock price increases over the exercise price by more than the premium paid, he will profit. If the stock price decreases, he will let the call contract expire worthless, and only lose the amount of the premium. A trader might buy the option instead of shares, because for the same amount of money, he can obtain a larger number of options than shares. If the stock rises, he will thus realize a larger gain than if he had purchased shares. This is an example of the principle of leverage.
Short Call (Naked short call)
A trader who believes that a stock's price will decrease can short sell the stock or instead sell a call. Both tactics are generally considered inappropriate for small investors. The trader selling a call has an obligation to sell the stock to the call buyer at the buyer's option. If the stock price decreases, the short call position will make a profit in the amount of the premium. If the stock price increases over the exercise price by more than the amount of the premium, the short will lose money. Unless a trader already owns the shares which he may be required to provide, the potential loss is unlimited. However, such a trader who sells a call option for those shares he already owns has sold a covered call.
Long Put
A trader who believes that a stock's price will decrease can buy the right to sell the stock at a fixed price. He will be under no obligation to sell the stock, but has the right to do so until the expiry date. If the stock price decreases below the exercise price by more than the premium paid, he will profit. If the stock price increases, he will just let the put contract expire worthless and only lose his premium paid.
Short Put (Naked put)
A trader who believes that a stock's price will increase can sell the right to sell the stock at a fixed price. The trader now has the obligation to purchase the stock at a fixed price. The trader has sold insurance to the buyer of the put requiring the trader to insure the stockholder below the fixed price. This trade is generally considered inappropriate for a small investor. If the stock price increases, the short put position will make a profit in the amount of the premium. If the stock price decreases below the exercise price by more than the premium, the short position will lose money.

Introduction to option strategies

Combining any of the four basic kinds of option trades (possibly with different exercise prices) and the two basic kinds of stock trades (long and short) allows a variety of options strategies. Simple strategies usually combine only a few trades, while more complicated strategies can combine several.

  • Covered call — Long the stock, short a call. This has essentially the same payoff as a short put.
  • Straddle — Long a call and long a put with the same exercise prices (a long straddle), or short a call and short a put with the same exercise prices (a short straddle).
  • Strangle — Long a call and long a put with different exercise prices (a long strangle), or short a call and short a put with different exercise prices (a short strangle).
  • Bull spread — Long a call with a low exercise price and short a call with a higher exercise price, or long a put with a low exercise price and short a put with a higher exercise price.
  • Bear spread — Short a call with a low exercise price and long a call with a higher exercise price, or short a put with a low exercise price and long a put with a higher exercise price.
  • Butterfly — Butterflies require trading options with 3 different exercise prices. Assume exercise prices X1 < X2 < X3 and that (X1 + X3) /2 = X2
    • Long butterfly — long 1 call with exercise price X1, short 2 calls with exercise price X2, and long 1 call with exercise price X3. Alternatively, long 1 put with exercise price X1, short 2 puts with exercise price X2, and long 1 put with exercise price X3.
    • Short butterfly — short 1 call with exercise price X1, long 2 calls with exercise price X2, and short 1 call with exercise price X3. Alternatively, short 1 put with exercise price X1, long 2 puts with exercise price X2, and short 1 put with exercise price X3.
  • Box spreads — Any combination of options that has a constant payoff at expiration. For example combining a long butterfly made with calls, with a short butterfly made with puts will have a constant payoff of zero, and in equilibrium will cost zero. In practice any profit from these spreads will be eaten up by commissions (hence the name "alligator spreads").

Historical uses of options

Contracts similar to options are believed to have been used since ancient times. 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 he can buy all the plots in the entire parcel. Film or theatrical producers often buy 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.

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.


  • Binomial options model
  • Black-Scholes
  • Black model
  • Call option
  • Covered call
  • Moneyness
  • Naked put
  • Option adjusted spread
  • Option time value
  • Option style
  • Put option
  • Put-call parity
  • Volatility smile

See also

  • CBOE
  • Derivative (finance)
  • Derivatives markets
  • Financial economics
  • Financial instruments
  • Finance
  • Futures contracts
  • Option screeners
  • Options backdating


  • Binary option
  • Bond option
  • Credit default option
  • Employee stock option
  • Exotic interest rate option
  • Foreign exchange option
  • Interest rate cap and floor
  • Options on futures
  • Options symbols
  • Real option
  • Swaption
  • Warrant


  • Kleinert, Hagen, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 4th edition, World Scientific (Singapore, 2004); Paperback ISBN 981-238-107-4 (also available online: PDF-files)
  • Investigation of Companies for Manipulating Stock Option Grants -
  • Options Backdating Information Center - ISS Comprehensive Information and Articles on the Options Backdating Scandal
  • Disk Lectures, Options I audio lecture with slideshow
  • Shares and share unlike - 1999 article from The Economist questioning whether investors (as owners) actually gain from large option packages for top management.
  • Erik Lie and Randall A. Heron, Does backdating explain the stock price pattern around executive stock option grants? PDF, Journal of Financial Economics, 2006.
  • Are CEOs Paid for Luck, Marianne Bertrand and Sendhil Mullainathan, Quarterly journal of Economics, 2001.
  • Are CEOs paid like Bureaucrats?, Brian Hall & Jeffrey Liebman, Quarterly journal of Economics, 1998.

External links

  • Gamma-Delta Neutral Option Spreads An academic paper outlining a neutral options strategy that goes in depth about various option characteristics
  • Option Clearing Corporation's Characteristics and Risks of Standardized Options, practical description of U.S.-based exchange-traded options
  • List of equities with options
  • Option Calculator
  • Investopedia, Options tutorial
  • 2006 Options Expiration Calendar
  • 2007 Options Expiration Calendar


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