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In finance, the **strike price** (or **exercise price**) of an option is the fixed price at which the owner of the option can buy (in the case of a call), or sell (in the case of a put), the underlying security or commodity. 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 taken out, or it may be fixed at a discount or at a premium.

**Finance** is a field that is concerned with the allocation (investment) of assets and liabilities over space and time, often under conditions of risk or uncertainty. Finance can also be defined as the art of money management. Participants in the market aim to price assets based on their risk level, fundamental value, and their expected rate of return. Finance can be split into three sub-categories: public finance, corporate finance and personal finance.

In finance, an **option** is a contract which gives the buyer the right, but not the obligation, to buy or sell an underlying asset or instrument at a specified strike price prior to or on a specified date, depending on the form of the option. The strike price may be set by reference to the spot price of the underlying security or commodity on the day an option is taken out, or it may be fixed at a discount or at a premium. The seller has the corresponding obligation to fulfill the transaction – to sell or buy – if the buyer (owner) "exercises" the option. An option that conveys to the owner the right to buy at a specific price is referred to as a call; an option that conveys the right of the owner to sell at a specific price is referred to as a put. Both are commonly traded, but the call option is more frequently discussed.

A **call option**, often simply labeled a "call", is a financial contract between two parties, the buyer and the seller of this type of option. The buyer of the call option has the right, but not the obligation, to buy an agreed quantity of a particular commodity or financial instrument from the seller of the option at a certain time for a certain price. The seller is obligated to sell the commodity or financial instrument to the buyer if the buyer so decides. The buyer pays a fee for this right. The term "call" comes from the fact that the owner has the right to "call the stock away" from the seller.

The strike price is a key variable in a derivatives contract between two parties. Where the contract requires delivery of the underlying instrument, the trade will be at the strike price, regardless of the market price of the underlying instrument at that time.

In finance, a **derivative** is a contract that *derives* its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation or getting access to otherwise hard-to-trade assets or markets. Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the New York Stock Exchange, while most insurance contracts have developed into a separate industry. In the United States, after the financial crisis of 2007–2009, there has been increased pressure to move derivatives to trade on exchanges. Derivatives are one of the three main categories of financial instruments, the other two being stocks and debt. The oldest example of a derivative in history, attested to by Aristotle, is thought to be a contract transaction of olives, entered into by ancient Greek philosopher Thales, who made a profit in the exchange. Bucket shops, outlawed a century ago, are a more recent historical example.

In finance, the **underlying** of a derivative is an asset, basket of assets, index, or even another derivative, such that the cash flows of the (former) derivative depend on the value of this underlying. There must be an independent way to observe this value to avoid conflicts of interest.

Moneyness is the value of a financial contract if the contract settlement is financial. More specifically, it is the difference between the strike price of the option and the current trading price of its underlying security.

In finance, **moneyness** is the relative position of the current price of an underlying asset with respect to the strike price of a derivative, most commonly a call option or a put option. Moneyness is firstly a three-fold classification: if the derivative would have positive intrinsic value if it were to expire today, it is said to be **in the money**; if it would be worthless if expiring at the current price it is said to be **out of the money**, and if the current price and strike price are equal, it is said to be **at the money**. There are two slightly different definitions, according to whether one uses the current price (spot) or future price (forward), specified as "at the money spot" or "at the money forward", etc.

In options trading, terms such as *in-the-money*, *at-the-money* and *out-of-the-money* describe the moneyness of options.

- A call option is in-the-money if the strike price is below the market price of the underlying stock.
- A put option is in-the-money if the strike price is above the market price of the underlying stock.

- A call or put option is at-the-money if the stock price and the exercise price are the same (or close).
- A call option is out-of-the-money if the strike price is above the market price of the underlying stock.
- A put option is out-of-the-money if the strike price is below the market price of the underlying stock.

A call option has positive monetary value at expiration when the underlying has a spot price (**S**) *above* the strike price (**K**). Since the option will not be exercised unless it is in-the-money, the payoff for a call option is

also written as

where

A put option has positive monetary value at expiration when the underlying has a spot price *below* the strike price; it is "out-the-money" otherwise, and will not be exercised. The payoff is therefore:

In finance, a **put** or **put option** is a stock market device which gives the owner the right, but not the obligation, to sell an asset, at a specified price, by a predetermined date to a given party. 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.

or

For a digital option payoff is , where is the indicator function:

The **Black–Scholes** or **Black–Scholes–Merton model** is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the **Black–Scholes formula**, which gives a theoretical estimate of the price of European-style options and shows that the option has a *unique* price regardless of the risk of the security and its expected return. The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. It is widely used, although often with some adjustments, by options market participants.

In financial mathematics, **put–call parity** defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to a single forward contract at this strike price and expiry. This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be purchased for the strike price, exactly as in a forward contract.

In finance, a **warrant** is a security that entitles the holder to buy the underlying stock of the issuing company at a fixed price called **exercise price** until the expiry date.

In 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.

The **Black model** is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond options, Interest rate cap and floors, and swaptions. It was first presented in a paper written by Fischer Black in 1976.

In finance, the **binomial options pricing model** (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting.

In mathematical finance, the **Greeks** are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters. Collectively these have also been called the **risk sensitivities**, **risk measures** or **hedge parameters**.

In finance, the **time value** (**TV**) of an option is the premium a rational investor would pay over its *current* exercise value, based on the probability it will increase in value before expiry. For an American option this value is always greater than zero in a fair market, thus an option is *always* worth more than its current exercise value.. As an option can be thought of as 'price insurance', TV can be thought of as the *risk premium* the option seller charges the buyer—the higher the expected risk, the higher the premium. Conversely, TV can be thought of as the price an investor is willing to pay for potential upside.

An **Asian option** is a special type of option contract. For Asian options the payoff is determined by the average underlying price over some pre-set period of time. This is different from the case of the usual European option and American option, where the payoff of the option contract depends on the price of the underlying instrument at exercise; Asian options are thus one of the basic forms of exotic options. There are two types of Asian options, the Fixed Strike-where averaging price is used in place of underlying price, and Fixed Price-where averaging price is used in place of strike.

**Lookback options**, in the terminology of finance, are a type of exotic option with path dependency, among many other kind of options. The payoff depends on the optimal underlying asset's price occurring over the life of the option. The option allows the holder to "look back" over time to determine the payoff. There exist two kinds of lookback options: with floating strike and with fixed strike.

In finance, a **foreign exchange option** is a derivative financial instrument that gives the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified date. See Foreign exchange derivative.

**Volatility smiles** are implied volatility patterns that arise in pricing financial options. It corresponds to finding one single parameter that is needed to be modified for the Black–Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money.

A **variance swap** is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the magnitude of movement, i.e. volatility, of some underlying product, like an exchange rate, interest rate, or stock index.

In options trading, a **box spread** is a combination of positions that has a certain payoff, considered to be simply "delta neutral interest rate position". For example, a bull spread constructed from calls combined with a bear spread constructed from puts has a constant payoff of the difference in exercise prices assuming that the underlying stock does not go ex-dividend before the expiration of the options. If the underlying asset has a dividend of x, then the settled value of the box will be 10+x. Under the no-arbitrage assumption, the net premium paid out to acquire this position should be equal to the present value of the payoff.

The **backspread** is the converse strategy to the ratio spread and is also known as reverse ratio spread. Using calls, a bullish strategy known as the call backspread can be constructed and with puts, a strategy known as the put backspread can be constructed.

**Rainbow option** is a derivative exposed to two or more sources of uncertainty, as opposed to a simple option that is exposed to one source of uncertainty, such as the price of underlying asset.

A **compound option** or **split-fee option** is an option on an option. The exercise payoff of a compound option involves the value of another option. A compound option then has two expiration dates and two strike prices. Usually, compounded options are used for currency or fixed income markets where insecurity exists regarding the option’s risk protection. Another common business application that compound options are used for is to hedge bids for business projects that may or may not be accepted.

In finance, a **synthetic position** is a way to create the payoff of a financial instrument using other financial instruments.

- McMillan, Lawrence G. (2002).
*Options as a Strategic Investment*(4th ed.). New York : New York Institute of Finance. ISBN 0-7352-0197-8.

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