Options Glossary

This is a glossary of common terms used in Option Theory.

American Option
An option that can only be exercised at any point before it's expiration. This is the most common type of option that is traded.

Arbitrage
The process in which equivalent securities are traded for a risk-less profit.

Ask
The price at which a market maker or broker is offering to sell an option or a stock.

Assignment
If you sold an call option that was exercised and you have been assigned, then you are obligated to sell the underlying at the specified strike price.
If you sold a put option that was exercised and you have been assigned, then you are obligated to buy the underlying at the specified strike price.

At-the-money (ATM)
An option is at-the-money if the strike price of the option is equal to (or very near to) the market price of the underlying.

Automatic Exercise
This is a protective procedure in which an option is automatically exercised if it expires ITM.

Backspread
An option strategy that is delta neutral and composed of more long options than short options. This position typically profits from a large movement in either direction in the underlying.

Bear Spread
This is an option strategy that makes its maximum profit when the underlying declines, and has the most risk when the underlying increases. An option on a higher strike is purchased and an option on a lower strike is sold. This can be done with (both) calls or puts.

Beta
A measure of how a stock's movement correlates to the movement of the entire stock market.

Bid
The price at which a market maker or broker is willing to buy an option or a stock.

Binomial Tree Method
A generalizable numerical method to value an option. It uses a discrete-time model of the underlying price over time. It does not have a closed-form solution, and requires constant recalculation. It is able to handle a wider varity of conditions which the other models are unable to deal with, and is often used to price complicated options. It is computationally slow, with a runtime of \( O (2^n) \).

Black-Scholes formula
The first widely used model to price an option. The inputs of the model are the current stock price, volatility and expected dividends, option's strike price and time to expiration, and expected interest rates. it makes several theoretical assumptions which do not accurately reflect real-world options markets, but is often used to value an option and to determine the implied volatility.

Option Payoff Diagrams
The price(s) at which an option strategy results in neither a profit nor a loss on expiration. A theoretical pricing model can be used to determine the option strategy's break even points at other dates.

Bull Spread
An option strategy that makes its maximum profit when the underlying rises, and has the most risk when the underlying decreases. An option on a lower strike is purchased and an option on a higher strike is sold. This can be done with (both) calls or puts.

Butterfly
An option strategy involving 3 strike prices: long 1 contract on the lowest strike, short 2 contracts on the middle strike, long 1 contract on the highest strike. it has limited risk and limited profit, and benefits the most when the underlying expires at the short strike.

Calendar Spread
An option strategy in which a short-term option is sold, and a long-term option is bought, with both having the same strike price. This can be done with call or puts.

Call option
An option contact that gives the owner the right (not obligation) to buy the underlying security at a specified price at a specified time.

Call Spread
An option strategy of buying a call on a lower strike and selling another call on a higher strike of the same expiry.

Carrying cost
The interest expense on a debit balance created by establishing a position.

Cash-based
An option or future that is settled in cash when exercised or assigned. No physical delivery is required.

Charm
A measure of the rate of change in an option's delta for a unit change in time.

Class of Options
A list of option contracts of the same type (call or put) and style (American or European) in the same underlying.

Collar
A protective strategy for owning a stock, in which an investor sells an upside call and buys a downside put.

Combination
Any position that involved put and call options in some quantity.

Condor
An option strategy involving 4 strike prices: long the lowest strike, short the second and third strike, long the highest strike. it has limited risk and limited profit, and benefits the most when the underlying expired between the two short strikes.

Contra-Exercise
The procedure in which an option that expired ITM is not exercised. This could be due to movements in the underlying during after hours.

Contract size
The amount of the underlying asset covered by the option contract. For equity options, this is typically 100 shares in the US. For future options, this is typically 1 future contract. It can be adjusted by a special even like a stock split.

Conversion
An option strategy of being long a put and short a call with the same strike price and expiration.

Covered call
An option strategy in which a call is sold against a long underlying position.

Covered Put
An option strategy in which a put is sold against a short underlying position.

Delivery
The process in which a call or put assignment is fulfilled. The underlying (stock or physical commodity) will have to be transferred to the buyer, under certain conditions.

Delta Spread
This is a ratio spread that establishes a neutral delta position.

Delta
The amount by which an option's price will change for a $1 price change in the underlying. This is an instantaneous measure of the option's price change.

Derivative security
A financial security whose value is determined from the value and characteristics of another security, which is known as the underlying.

Diagonal Spread
A spread in which the purchased options have a longer maturity than the sold options.

Discount
An option is trading at a discount if it is trading for less than its intrinsic value.

Dividend Risk
A measure of the rate of change in an option's theoretical value for a unit change in the dividend.

Downside
Below the current underlying price.

Early Exercise
The exercise or assignment of an option contract before its expiration date.

European Option
An option that can only be exercised at its expiration. There is no possibility of early exercise / assignment of this option, though it is still subject to contra-exercise.

Ex-Dividend
The process by which a stock's price is reduced when a dividend is paid. The ex-dividend date (or ex-date) is the date on which this occurs. Investors who own the stock on the ex-date will receive the dividend, while those who are short the short will have to pay the dividend.

Exercise
The process in which the right of the holder of an option is implemented.

Expiration time
The time of day by which all exercise notices must be received on the expiration date.
Technically, this occurs at 5:00 PM EST to coincide with the close of the market. However, owners of option contracts have up to 5:30 PM (or later) to decide if they would like to contra-exercise.

Extrinsic Value / Time Value
The portion of the option premium that is attributable to the amount of time remaining until the expiration of the option contract. Extrinsic value is equal to the option value minus the intrinsic value.

Finite Difference Method
An option valuation method which approximates the continuous-time differential equation to solve the discrete difference equations iteratively to calculate an option price. This is a more general case of the Binomial Tree method.

Floor Broker
A broker on the exchange floor who executes the orders of public customers or other investors who do not have physical access to the trading area.

Forward
The expected price of an underlying at some point in the future.

Forward contract
A non-standardized contract between two parties, to trade an asset at a specified price, and at a specified future date.

Fungible
Securities that are interchangeable because they have been standardized. OTC options are generally not fungible. Options that are listed on national exchanges are fungible.

Futures / Futures contract
A standardized contract calling for the delivery of a specified quantity of a commodity, at a specified date in the future.

Gamma
The amount by which an option's delta will change for a $1 price change in the underlying. This is an instantaneous measure of the option's delta change.

Hedge ratio
The amount of stock that has to be sold in order to maintain a delta neutral position.

Historical Volatility
A measure of the volatility of the underlying, based on historical data of the price changes of the underlying.

Horizontal spread
An option strategy in which options have the same strike price, but different expiration dates.

Implied Volatility
A measure of the volatility of the underlying. It is determined by using current option prices in the market.

In-the-money (ITM)
An option is in-the-money if it has intrinsic value. A call option is ITM if the underlying price is higher than the strike price, while a put option is ITM if the underlying price is lower than the strike price.

Index Option
An option whose underlying is an index. Most index options are cash-based.

Intrinsic Value
The value of an option arising because it is in-the-money. This would be the value of the option if it were to expire immediately. For call options, this is equal to \( \max(S-X, 0) \). For put options, this is equal to \( \max (X-S, 0 ) \).

Leg
1. A risky method of establishing a two-sided position, where one side of the position is executed first, as opposed to simultaneous execution. The risk comes from the fact that a better / similar price for the other side of the position might not be achieved.
2. Any part of an option strategy.

Leverage
Obtaining a greater percentage profit and risk potential.

Lognormal distribution
A statistical distribution that is often applied to the movement of stock prices. It implies that stock prices can theoretically rise indefinitely, but can never fall below zero. It has been established that stock movements have greater extreme movements than that predicted by a lognormal distribution.

Long position
A position in which an investor is a net holder of option contracts (typically, but not always).

Margin Requirements
The amount an uncovered option writer is required to deposit and maintain to cover a position. This margin requirement is calculated daily.

Margin
Buying a security by borrowing funds from a brokerage house.

Market-Maker
An exchange member whose function is to provide continuous bid and ask quotes, even in the absence of public buy or sell orders.

Model
A mathematical formula used to price an option, based on various variables as inputs. The Black-Scholes model is one of the most commonly used models.

Monte-Carlo Analysis
The Monte Carlo method is a technique of statistical sampling that is employed to approximate solutions to quantitative problems. It directly simulates the underlying process, and then calculates the average result of the process over several trials. This allows it to model a stochastic/probabilistic approach. It has a polynomial run-time, and is often used to model American options.

Neutral strategy
Neutral option strategies are generally designed to perform best if there is little change in the price of the underlying.

Option Pricing Curve
This is a graph of the projected price of an option as the underlying moves. It reflects the amount of time value premium at each underlying price. The delta can be calculated as the slope of the tangent line to the curve at a given price.

Option Greeks
Risk measures of an option strategy, which explains how option prices change due to a change in the underlying price, volatility or time decay.

Option Value
The price of an option. It consists of the intrinsic value and the extrinsic value.

Out-of-the-money (OTM)
An option is out-of-the-money if it has no intrinsic value. A call option is OTM if the underlying price is lower than the strike price, while a put option is OTM if the underlying price is higher than the strike price.

Over-the-counter (OTC)
A security that is not traded at an exchange, but is traded directly between a buyer and a seller. There is often no secondary market, and the contract parameters have not been standardized.

Parity
An ITM option is trading at parity if i is trading for its intrinsic value. Equivalently, there is no extrinsic value to the option.

Payoff Diagram
A graphical representation of the potential outcomes of a strategy. The amount of profit/loss is graphed on the vertical axis, against stock price on the horizontal axis. This graph usually depicts results at expiration of the options.

Premium
The price of an option contract, which the buyer pays to the seller.

Profit range
The range within which a particular position makes a profit.

Put Call Parity
An important fundamental relationship between the price of the underlying assets, and a (European) put and call of the same strike and time to expiry. It states that \( C - P = S - K e^{-rt} \).

Put option
An option contact that gives the owner the right (not obligation) to sell the underlying security at a specified price at a specified time.

Put Spread An option strategy of buying a put on a higher strike and selling another put on a lower strike of the same expiry.

Ratio spread
An option strategy which consists of buying some options, and then selling a larger quantity of options that are more out-of-the-money.

Ratio write
Selling of call options in a ratio that is higher than 1 to 1 against the stock that is owned.

Return
The percentage profit that is (will be) made on an investment.

Reversal / Risk Reversal / Risky
An option strategy of being long a call and short a put with the same strike price and expiration.

Rho
The expected change in the options's theoretical value for a 2% increase in interest rate.

Roll
Closing a currently open position, and opening up an option position with different terms, on the same underlying. A position can be rolled forward into a later expiry, rolled up to a higher strike, or rolled down to a lower strike.

Series
All option contracts of the same class that have the same unit of trade, expiration date, and strike price.

Settlement Price
This is the official published price at the end of a trading session. Option prices are established by the Options Clearing Corporation and is used to determine account equity and balance, margin requirements, and other purposes.

Short position
A position where an investor is a net seller of option contracts (typically, but not always).

Spread Strategy
An option position with both long and short options of the same type on the same underlying.

Standard deviation
A measure of volatility; it measures the magnitude of daily price changes.

Straddle
The purchase of an equal number of calls and puts with the same terms (strike and expiry).

Straddle Approximation Formula
This formula provides the approximate value of an ATM straddle. It is given by \( k S \sigma \sqrt{t} \), where the constant depends on the units used.

Strangle
The purchase of an equal number of calls and puts with different strikes, and the same time to expiry.

Synthetic Call
An option strategy of buying the stock and buying a put, which is equivalent to purchasing a call option.

Synthetic Put
An option strategy of selling the stock an purchasing a call, which is equivalent to purchasing a put option.

Theoretical Value
The price of an option computed from a mathematical model.

Theta
A measure of the rate of change in an option's theoretical value for a unit change in time. It is negative for options, indicating that option prices decrease over time.

Time Decay
This describes how the theoretical value of an option decreases with the passage of time.

Uncovered option
A short option position is uncovered if the investor does not have an offsetting position in the underlying.

Underlying security
The security that is being purchased or sold when the option contact is exercised.

Upside
Above the current underlying price.

Vanna
A measure of the rate of change in an options' delta for a unit change in volatility.

Vega
A measure of the rate of change in an option's theoretical value for a unit change in volatility.

Vertical spread
1. Commonly refers to a 1-1 call spread or put spread.
2. A delta-neutral spread in which more options are sold than are purchased.

Volatility
A measure of the fluctuation in the market price of the underlying security. It is the annualized standard deviation of returns.

Vomma
A measure of the rate of change in an options' vega for a unit change in volatility.

Write option
Selling an option. An investor who sells an option is called a writer.